{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,25]],"date-time":"2026-02-25T00:27:39Z","timestamp":1771979259707,"version":"3.50.1"},"reference-count":20,"publisher":"AIP Publishing","issue":"12","funder":[{"name":"Funda\u00e7\u00e3o para a ci\u00eancia e tecnologia, Portugal","award":["UIDB\/00208\/2020"],"award-info":[{"award-number":["UIDB\/00208\/2020"]}]}],"content-domain":{"domain":["pubs.aip.org"],"crossmark-restriction":true},"short-container-title":[],"published-print":{"date-parts":[[2023,12,1]]},"abstract":"<jats:p>We show the existence of classes of non-tiling domains satisfying P\u00f3lya\u2019s conjecture in any dimension, in both the Euclidean and non-Euclidean cases. This is a consequence of a more general observation asserting that if a domain satisfies P\u00f3lya\u2019s conjecture eventually, that is, for a sufficiently large order of the eigenvalues, and may be partioned into p non-overlapping isometric sub-domains, with p arbitrarily large, then there exists an order p0 such that for p larger than p0 all such sub-domains satisfy P\u00f3lya\u2019s conjecture. In particular, this allows us to show that families of sectors of domains of revolution with analytic boundary, and thin cylinders satisfy P\u00f3lya\u2019s conjecture, for instance. We also improve upon the Li\u2013Yau constant for general cylinders in the Dirichlet case.<\/jats:p>","DOI":"10.1063\/5.0161050","type":"journal-article","created":{"date-parts":[[2023,12,4]],"date-time":"2023-12-04T11:27:09Z","timestamp":1701689229000},"update-policy":"https:\/\/doi.org\/10.1063\/aip-crossmark-policy-page","source":"Crossref","is-referenced-by-count":5,"title":["Families of non-tiling domains satisfying P\u00f3lya\u2019s conjecture"],"prefix":"10.1063","volume":"64","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-2007-5259","authenticated-orcid":false,"given":"P.","family":"Freitas","sequence":"first","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa , Campo Grande, Edif\u00edcio C6, 1749-016 Lisboa, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2858-0823","authenticated-orcid":false,"given":"I.","family":"Salavessa","sequence":"additional","affiliation":[{"name":"Grupo de F\u00edsica Matem\u00e1tica, Faculdade de Ci\u00eancias, Universidade de Lisboa , Campo Grande, Edif\u00edcio C6, 1749-016 Lisboa, Portugal"}]}],"member":"317","published-online":{"date-parts":[[2023,12,4]]},"reference":[{"key":"2023120411270026400_c1","doi-asserted-by":"publisher","first-page":"1134","DOI":"10.1070\/IM1972v006n05ABEH001913","article-title":"Covariant and contravariant symbols of operators","volume":"36","year":"1972","journal-title":"Izv. 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