{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T14:34:54Z","timestamp":1773671694625,"version":"3.50.1"},"reference-count":20,"publisher":"American Mathematical Society (AMS)","license":[{"start":{"date-parts":[[2026,10,27]],"date-time":"2026-10-27T00:00:00Z","timestamp":1793059200000},"content-version":"am","delay-in-days":365,"URL":"https:\/\/www.ams.org\/publications\/copyright-and-permissions"}],"funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00208\/2023"],"award-info":[{"award-number":["UID\/00208\/2023"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2023.13921.PEX"],"award-info":[{"award-number":["2023.13921.PEX"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00208\/2023"],"award-info":[{"award-number":["UID\/00208\/2023"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2023.13921.PEX"],"award-info":[{"award-number":["2023.13921.PEX"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00208\/2023"],"award-info":[{"award-number":["UID\/00208\/2023"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2023.13921.PEX"],"award-info":[{"award-number":["2023.13921.PEX"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/00208\/2023"],"award-info":[{"award-number":["UID\/00208\/2023"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UIDB\/04106\/2020"],"award-info":[{"award-number":["UIDB\/04106\/2020"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["2023.13921.PEX"],"award-info":[{"award-number":["2023.13921.PEX"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Proc. Amer. Math. Soc."],"abstract":"<p>\n                    Inspired by a recent result of Funano\u2019s, we provide a sharp quantitative comparison result between the first nontrivial eigenvalues of the Neumann Laplacian on bounded convex domains\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"normal upper Omega 1 subset-of normal upper Omega 2\">\n                        <mml:semantics>\n                          <mml:mrow>\n                            <mml:msub>\n                              <mml:mi mathvariant=\"normal\">\n                                \u03a9\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>1<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                            <mml:mo>\n                              \u2282\n                              \n                            <\/mml:mo>\n                            <mml:msub>\n                              <mml:mi mathvariant=\"normal\">\n                                \u03a9\n                                \n                              <\/mml:mi>\n                              <mml:mrow class=\"MJX-TeXAtom-ORD\">\n                                <mml:mn>2<\/mml:mn>\n                              <\/mml:mrow>\n                            <\/mml:msub>\n                          <\/mml:mrow>\n                          <mml:annotation encoding=\"application\/x-tex\">\\Omega _{1} \\subset \\Omega _{2}<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    in any dimension\n                    <inline-formula content-type=\"math\/mathml\">\n                      <mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" alttext=\"d\">\n                        <mml:semantics>\n                          <mml:mi>d<\/mml:mi>\n                          <mml:annotation encoding=\"application\/x-tex\">d<\/mml:annotation>\n                        <\/mml:semantics>\n                      <\/mml:math>\n                    <\/inline-formula>\n                    greater than or equal to two, recovering domain monotonicity up to an explicit multiplicative factor. We provide upper and lower bounds for such multiplicative factors for higher-order eigenvalues, and study their behaviour with respect to the dimension and order. We further consider different scenarios where convexity is no longer imposed. In a final section we formulate some related open problems.\n                  <\/p>","DOI":"10.1090\/proc\/17394","type":"journal-article","created":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T19:00:33Z","timestamp":1761591633000},"source":"Crossref","is-referenced-by-count":0,"title":["On domain monotonicity of Neumann eigenvalues of convex domains"],"prefix":"10.1090","author":[{"given":"Pedro","family":"Freitas","sequence":"first","affiliation":[]},{"given":"James","family":"Kennedy","sequence":"additional","affiliation":[]}],"member":"14","published-online":{"date-parts":[[2025,10,27]]},"reference":[{"issue":"1","key":"1","doi-asserted-by":"publisher","first-page":"235","DOI":"10.1007\/s10957-011-9983-3","article-title":"Numerical optimization of low eigenvalues of the Dirichlet and Neumann Laplacians","volume":"154","author":"Antunes, Pedro R. S.","year":"2012","journal-title":"J. Optim. Theory Appl.","ISSN":"https:\/\/id.crossref.org\/issn\/0022-3239","issn-type":"print"},{"key":"2","doi-asserted-by":"publisher","first-page":"398","DOI":"10.1515\/9783110550887-011","article-title":"Numerical results for extremal problem for eigenvalues of the Laplacian","author":"Antunes, Pedro R. S.","year":"2017"},{"issue":"4","key":"3","doi-asserted-by":"publisher","first-page":"751","DOI":"10.4171\/ZAA\/1170","article-title":"A note on the Poincar\u00e9 inequality for convex domains","volume":"22","author":"Bebendorf, M.","year":"2003","journal-title":"Z. Anal. Anwendungen","ISSN":"https:\/\/id.crossref.org\/issn\/0232-2064","issn-type":"print"},{"issue":"6","key":"4","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1090\/S0002-9904-1897-00397-4","article-title":"On certain methods of Sturm and their application to the roots of Bessel\u2019s functions","volume":"3","author":"B\u00f4cher, Maxime","year":"1897","journal-title":"Bull. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9904","issn-type":"print"},{"issue":"2","key":"5","doi-asserted-by":"publisher","first-page":"337","DOI":"10.4310\/ACTA.2019.v222.n2.a2","article-title":"Maximization of the second non-trivial Neumann eigenvalue","volume":"222","author":"Bucur, Dorin","year":"2019","journal-title":"Acta Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0001-5962","issn-type":"print"},{"key":"6","series-title":"Pure and Applied Mathematics","isbn-type":"print","volume-title":"Eigenvalues in Riemannian geometry","volume":"115","author":"Chavel, Isaac","year":"1984","ISBN":"https:\/\/id.crossref.org\/isbn\/0121706400"},{"issue":"1-2","key":"7","doi-asserted-by":"publisher","first-page":"529","DOI":"10.1007\/s00209-014-1325-3","article-title":"Extremal eigenvalues of the Laplacian on Euclidean domains and closed surfaces","volume":"278","author":"Colbois, Bruno","year":"2014","journal-title":"Math. Z.","ISSN":"https:\/\/id.crossref.org\/issn\/0025-5874","issn-type":"print"},{"issue":"3","key":"8","doi-asserted-by":"publisher","first-page":"537","DOI":"10.1002\/cpa.22231","article-title":"On the P\u00f3lya conjecture for the Neumann problem in planar convex domains","volume":"78","author":"Filonov, N.","year":"2025","journal-title":"Comm. Pure Appl. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0010-3640","issn-type":"print"},{"key":"9","unstructured":"N. Filonov, private communication, September 11, 2023."},{"issue":"1","key":"10","doi-asserted-by":"publisher","first-page":"317","DOI":"10.1515\/agms-2016-0015","article-title":"Applications of the \u2018ham sandwich theorem\u2019 to eigenvalues of the Laplacian","volume":"4","author":"Funano, Kei","year":"2016","journal-title":"Anal. Geom. Metr. Spaces"},{"issue":"4","key":"11","doi-asserted-by":"publisher","first-page":"677","DOI":"10.1215\/00192082-10972651","article-title":"A note on domain monotonicity for the Neumann eigenvalues of the Laplacian","volume":"67","author":"Funano, Kei","year":"2023","journal-title":"Illinois J. Math.","ISSN":"https:\/\/id.crossref.org\/issn\/0019-2082","issn-type":"print"},{"issue":"2","key":"12","doi-asserted-by":"publisher","first-page":"277","DOI":"10.1007\/s40316-023-00218-z","article-title":"Optimal bounds for Neumann eigenvalues in terms of the diameter","volume":"48","author":"Henrot, Antoine","year":"2024","journal-title":"Ann. Math. Qu\\'{e}.","ISSN":"https:\/\/id.crossref.org\/issn\/2195-4755","issn-type":"print"},{"issue":"3-4","key":"13","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1080\/00036818508839574","article-title":"A differential equation for the zeros of Bessel functions","volume":"20","author":"Ifantis, E. K.","year":"1985","journal-title":"Applicable Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0003-6811","issn-type":"print"},{"issue":"6","key":"14","doi-asserted-by":"publisher","first-page":"1665","DOI":"10.1090\/S0002-9939-99-04804-2","article-title":"On upper bounds for high order Neumann eigenvalues of convex domains in Euclidean space","volume":"127","author":"Kr\u00f6ger, Pawel","year":"1999","journal-title":"Proc. Amer. Math. Soc.","ISSN":"https:\/\/id.crossref.org\/issn\/0002-9939","issn-type":"print"},{"issue":"6","key":"15","doi-asserted-by":"publisher","first-page":"517","DOI":"10.1080\/1024123021000053664","article-title":"Eigenstructure of the equilateral triangle. II. The Neumann problem","volume":"8","author":"McCartin, Brian J.","year":"2002","journal-title":"Math. Probl. Eng.","ISSN":"https:\/\/id.crossref.org\/issn\/1024-123X","issn-type":"print"},{"key":"16","first-page":"215","article-title":"Bessel functions","author":"Olver, F. W. J.","year":"2010"},{"key":"17","doi-asserted-by":"publisher","first-page":"286","DOI":"10.1007\/BF00252910","article-title":"An optimal Poincar\u00e9 inequality for convex domains","volume":"5","author":"Payne, L. E.","year":"1960","journal-title":"Arch. Rational Mech. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/0003-9527","issn-type":"print"},{"key":"18","doi-asserted-by":"publisher","first-page":"343","DOI":"10.1512\/iumj.1954.3.53017","article-title":"Inequalities for certain eigenvalues of a membrane of given area","volume":"3","author":"Szeg\u00f6, G.","year":"1954","journal-title":"J. Rational Mech. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1943-5282","issn-type":"print"},{"key":"19","volume-title":"A Treatise on the Theory of Bessel Functions","author":"Watson, G. N.","year":"1944"},{"key":"20","doi-asserted-by":"publisher","first-page":"633","DOI":"10.1512\/iumj.1956.5.55021","article-title":"An isoperimetric inequality for the \ud835\udc41-dimensional free membrane problem","volume":"5","author":"Weinberger, H. F.","year":"1956","journal-title":"J. Rational Mech. Anal.","ISSN":"https:\/\/id.crossref.org\/issn\/1943-5282","issn-type":"print"}],"container-title":["Proceedings of the American Mathematical Society"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.ams.org\/proc\/0000-000-00\/S0002-9939-2025-17394-4\/proc17394_AM.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/www.ams.org\/proc\/0000-000-00\/S0002-9939-2025-17394-4\/S0002-9939-2025-17394-4.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,3,16]],"date-time":"2026-03-16T13:25:35Z","timestamp":1773667535000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.ams.org\/proc\/2025-153-12\/S0002-9939-2025-17394-4\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,27]]},"references-count":20,"alternative-id":["S0002-9939-2025-17394-4"],"URL":"https:\/\/doi.org\/10.1090\/proc\/17394","archive":["CLOCKSS","Portico"],"relation":{},"ISSN":["1088-6826","0002-9939"],"issn-type":[{"value":"1088-6826","type":"electronic"},{"value":"0002-9939","type":"print"}],"subject":[],"published":{"date-parts":[[2025,10,27]]}}}