{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T08:53:35Z","timestamp":1772268815078,"version":"3.50.1"},"reference-count":21,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2014,9,24]],"date-time":"2014-09-24T00:00:00Z","timestamp":1411516800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2014,12]]},"DOI":"10.1007\/s00454-014-9637-y","type":"journal-article","created":{"date-parts":[[2014,9,23]],"date-time":"2014-09-23T23:21:29Z","timestamp":1411514489000},"page":"806-823","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":21,"title":["On the Theory of Coconvex Bodies"],"prefix":"10.1007","volume":"52","author":[{"given":"Askold","family":"Khovanski\u012d","sequence":"first","affiliation":[]},{"given":"Vladlen","family":"Timorin","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2014,9,24]]},"reference":[{"key":"9637_CR1","unstructured":"Aleksandrov, A.D.: To the theory of mixed volumes of convex bodies II. New inequalities between mixed volumes and their applications. Mat. Sb. 2(6), 1205\u20131238 (1937) (in Russian)"},{"key":"9637_CR2","doi-asserted-by":"crossref","DOI":"10.1007\/978-1-4612-5154-5","volume-title":"Singularities of Differentiable Maps","author":"V Arnold","year":"1985","unstructured":"Arnold, V., Varchenko, A., Gusein-Zade, S.: Singularities of Differentiable Maps. Springer, New York (1985)"},{"key":"9637_CR3","volume-title":"Computing the Continuous Discretely","author":"M Beck","year":"2009","unstructured":"Beck, M., Robins, S.: Computing the Continuous Discretely. Springer, New York (2009)"},{"issue":"3","key":"9637_CR4","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1007\/BF01075595","volume":"9","author":"D Bernstein","year":"1975","unstructured":"Bernstein, D.: The number of roots of a system of equations. Funct. Anal. Appl. 9(3), 183\u2013185 (1975)","journal-title":"Funct. Anal. Appl."},{"issue":"4","key":"9637_CR5","doi-asserted-by":"crossref","first-page":"653","DOI":"10.24033\/asens.1572","volume":"21","author":"M Brion","year":"1988","unstructured":"Brion, M.: Points entiers dans les poly\u00e8dres convexes. Ann. Sci. \u00c9cole Norm. Sup. (4) 21(4), 653\u2013663 (1988)","journal-title":"Ann. Sci. \u00c9cole Norm. Sup. (4)"},{"key":"9637_CR6","unstructured":"Dubrovin, B.A., Novikov, S.P., Fomenko, A.T.: Modern Geometry: Methods and Applications, Part I. The Geometry of Surfaces, Transformation Groups, and Fields. Graduate Texts in Math., Vol. 93. Springer, New York (1991)"},{"key":"9637_CR7","unstructured":"Fillastre, F.: Fuchsian convex bodies: Basics of Brunn\u2013Minkowski theory. Geom. Funct. Anal. 23(1), 295\u2013333 (2013)"},{"issue":"2","key":"9637_CR8","doi-asserted-by":"crossref","first-page":"925","DOI":"10.4007\/annals.2012.176.2.5","volume":"176","author":"K Kaveh","year":"2012","unstructured":"Kaveh, K., Khovanski\u012d, A.G.: Newton\u2013Okounkov bodies, semigroups of integral points, graded algebras and intersection theory. Ann. Math. 176(2), 925\u2013978 (2012)","journal-title":"Ann. Math."},{"key":"9637_CR9","doi-asserted-by":"crossref","unstructured":"Kaveh, K., Khovanski\u012d, A.G.: Convex bodies and multiplicities of ideals. In: Proceedings of the Steklov Institute of Mathematics. Springer, New York (2013) (to appear)","DOI":"10.1134\/S0081543814060169"},{"key":"9637_CR10","unstructured":"Khovanskii, A.: Algebra and mixed volumes. In: Burago, Yu.D., Zalgaller, V.A. (eds.) Geometric Inequalities. Springer, Berlin (2010)"},{"issue":"2","key":"9637_CR11","first-page":"337","volume":"4","author":"A Khovanski\u012d","year":"1993","unstructured":"Khovanski\u012d, A., Pukhlikov, A.: Finitely additive measures of virtual polytopes. St. Petersburg Math. J. 4(2), 337\u2013356 (1993)","journal-title":"St. Petersburg Math. J."},{"issue":"4","key":"9637_CR12","first-page":"789","volume":"4","author":"A Khovanski\u012d","year":"1993","unstructured":"Khovanski\u012d, A., Pukhlikov, A.: The Riemann\u2013Roch theorem for integrals and sums of quasipolynomials on virtual polytopes. St. Petersburg Math. J. 4(4), 789\u2013812 (1993)","journal-title":"St. Petersburg Math. J."},{"key":"9637_CR13","unstructured":"Khovanski\u012d, A., Timorin, V.: Aleksandrov\u2013Fenchel inequality for coconvex bodies. http:\/\/arxiv.org\/abs\/1305.4484"},{"key":"9637_CR14","first-page":"122","volume":"32","author":"A Khovansky","year":"1985","unstructured":"Khovansky, A., Varchenko, A.: Asymptotics of integrals over vanishing cycles and the Newton polyhedron. Sov. Math. Dokl. 32, 122\u2013127 (1985)","journal-title":"Sov. Math. Dokl."},{"issue":"1","key":"9637_CR15","doi-asserted-by":"crossref","first-page":"71","DOI":"10.1007\/BF01078188","volume":"9","author":"A Kouchnirenko","year":"1975","unstructured":"Kouchnirenko, A.: Newton polyhedron and Milnor numbers. Funct. Anal. Appl. 9(1), 71\u201372 (1975)","journal-title":"Funct. Anal. Appl."},{"key":"9637_CR16","doi-asserted-by":"crossref","unstructured":"Martinez-Maure, Y.: Hedgehog theory via Euler calculus. Beitr. Algebra Geom. doi: 10.1007\/s13366-014-0196-4","DOI":"10.1007\/s13366-014-0196-4"},{"issue":"1","key":"9637_CR17","doi-asserted-by":"crossref","first-page":"113","DOI":"10.1112\/plms\/s3-35.1.113","volume":"35","author":"P McMullen","year":"1977","unstructured":"McMullen, P.: Valuations and Euler-type relations on certain classes of convex polytopes. Proc. Lond. Math. Soc. Ser. 3 35(1), 113\u2013135 (1977)","journal-title":"Proc. Lond. Math. Soc. Ser. 3"},{"key":"9637_CR18","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/BF01244313","volume":"113","author":"P McMullen","year":"1993","unstructured":"McMullen, P.: On simple polytopes. Invent. Math. 113, 419\u2013444 (1993)","journal-title":"Invent. Math."},{"key":"9637_CR19","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511526282","volume-title":"Convex Bodies: The Brunn\u2013Minkowski Theory","author":"R Schneider","year":"1993","unstructured":"Schneider, R.: Convex Bodies: The Brunn\u2013Minkowski Theory. Cambridge University Press, Cambridge (1993)"},{"issue":"4","key":"9637_CR20","first-page":"287","volume":"288","author":"B Teissier","year":"1979","unstructured":"Teissier, B.: Du th\u00e9or\u00e8me de l\u2019index de Hodge aux in\u00e9galit\u00e9s isop\u00e9rim\u00e9triques. C. R. Acad. Sci. Paris S\u00e9r. A 288(4), 287\u2013289 (1979)","journal-title":"C. R. Acad. Sci. Paris S\u00e9r. A"},{"issue":"2","key":"9637_CR21","doi-asserted-by":"crossref","first-page":"381","DOI":"10.1070\/RM1999v054n02ABEH000134","volume":"54","author":"V Timorin","year":"1999","unstructured":"Timorin, V.: An analogue of the Hodge\u2013Riemann relations for simple polytopes. Russ. Math. Surv. 54(2), 381\u2013426 (1999)","journal-title":"Russ. Math. Surv."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9637-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-014-9637-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-014-9637-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,8,15]],"date-time":"2019-08-15T09:16:00Z","timestamp":1565860560000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-014-9637-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014,9,24]]},"references-count":21,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2014,12]]}},"alternative-id":["9637"],"URL":"https:\/\/doi.org\/10.1007\/s00454-014-9637-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2014,9,24]]}}}