{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,2]],"date-time":"2026-03-02T06:22:25Z","timestamp":1772432545302,"version":"3.50.1"},"reference-count":18,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2008,8,19]],"date-time":"2008-08-19T00:00:00Z","timestamp":1219104000000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2008,12]]},"DOI":"10.1007\/s00454-008-9077-7","type":"journal-article","created":{"date-parts":[[2008,8,18]],"date-time":"2008-08-18T19:29:41Z","timestamp":1219087781000},"page":"561-585","source":"Crossref","is-referenced-by-count":11,"title":["A Variational Proof of Alexandrov\u2019s Convex Cap Theorem"],"prefix":"10.1007","volume":"40","author":[{"given":"Ivan","family":"Izmestiev","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2008,8,19]]},"reference":[{"key":"9077_CR1","series-title":"Springer Monographs in Mathematics","volume-title":"Convex Polyhedra","author":"A.D. Alexandrov","year":"2005","unstructured":"Alexandrov, A.D.: Convex Polyhedra. Springer Monographs in Mathematics. Springer, Berlin (2005)"},{"issue":"2","key":"9077_CR2","doi-asserted-by":"crossref","first-page":"447","DOI":"10.5802\/aif.2358","volume":"58","author":"A. Bobenko","year":"2008","unstructured":"Bobenko, A., Izmestiev, I.: Alexandrov\u2019s theorem, weighted Delaunay triangulations, and mixed volumes. Ann. Inst. Fourier (Grenoble) 58(2), 447\u2013505 (2008)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"issue":"2","key":"9077_CR3","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1090\/S0002-9947-03-03239-2","volume":"356","author":"A.I. Bobenko","year":"2004","unstructured":"Bobenko, A.I., Springborn, B.A.: Variational principles for circle patterns and Koebe\u2019s theorem. Trans. Am. Math. Soc. 356(2), 659\u2013689 (2004) (electronic)","journal-title":"Trans. Am. Math. Soc."},{"key":"9077_CR4","series-title":"Grundlehren der Mathematischen Wissenschaften","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-662-07441-1","volume-title":"Geometric Inequalities","author":"Y.D. Burago","year":"1988","unstructured":"Burago, Y.D., Zalgaller, V.A.: Geometric Inequalities. Grundlehren der Mathematischen Wissenschaften, vol.\u00a0285. Springer, Berlin (1988)"},{"key":"9077_CR5","first-page":"87","volume":"19","author":"A.-L. Cauchy","year":"1813","unstructured":"Cauchy, A.-L.: Sur les polygones et poly\u00e8dres, second m\u00e9moire. J. Ec. Polytech. 19, 87\u201398 (1813)","journal-title":"J. Ec. Polytech."},{"key":"9077_CR6","series-title":"Les Grands Classiques Gauthier-Villars","volume-title":"Le\u00e7ons sur la th\u00e9orie g\u00e9n\u00e9rale des surfaces. III, IV","author":"G. Darboux","year":"1993","unstructured":"Darboux, G.: Le\u00e7ons sur la th\u00e9orie g\u00e9n\u00e9rale des surfaces. III, IV. Les Grands Classiques Gauthier-Villars. \u00c9ditions Jacques Gabay, Sceaux (1993)"},{"key":"9077_CR7","doi-asserted-by":"crossref","first-page":"466","DOI":"10.1007\/BF01456962","volume":"77","author":"M. Dehn","year":"1916","unstructured":"Dehn, M.: \u00dcber die Starrheit konvexer Polyeder. Math. Ann. 77, 466\u2013473 (1916)","journal-title":"Math. Ann."},{"issue":"1","key":"9077_CR8","doi-asserted-by":"crossref","first-page":"163","DOI":"10.5802\/aif.2255","volume":"57","author":"F. Fillastre","year":"2007","unstructured":"Fillastre, F.: Polyhedral realization of hyperbolic metrics with conical singularities on compact surfaces. Ann. Inst. Fourier (Grenoble) 57(1), 163\u2013195 (2007)","journal-title":"Ann. Inst. Fourier (Grenoble)"},{"key":"9077_CR9","unstructured":"Fillastre, F., Izmestiev, I.: Hyperbolic cusps with convex polyhedral boundary. arXiv:0708.2666"},{"key":"9077_CR10","unstructured":"Fillastre, F., Izmestiev, I.: Dual metrics of hyperbolic cusps with convex polyhedral boundary (in preparation)"},{"issue":"1","key":"9077_CR11","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1007\/BF01231281","volume":"111","author":"C.D. Hodgson","year":"1993","unstructured":"Hodgson, C.D., Rivin, I.: A characterization of compact convex polyhedra in hyperbolic 3-space. Invent. Math. 111(1), 77\u2013111 (1993)","journal-title":"Invent. Math."},{"key":"9077_CR12","unstructured":"Luo, F.: Rigidity of polyhedral surfaces. arXiv:math.GT\/0612714"},{"key":"9077_CR13","first-page":"x+295","volume-title":"Collected Papers","author":"J. Milnor","year":"1994","unstructured":"Milnor, J.: The Schl\u00e4fli differential equality. In: Collected Papers, vol. 1, pp. x+295. Publish or Perish Inc., Houston (1994)"},{"issue":"1","key":"9077_CR14","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1007\/BF01448039","volume":"110","author":"R. Sauer","year":"1935","unstructured":"Sauer, R.: Projektive S\u00e4tze in der Statik des starren K\u00f6rpers. Math. Ann. 110(1), 464\u2013472 (1935)","journal-title":"Math. Ann."},{"key":"9077_CR15","unstructured":"Schlenker, J.-M.: On weakly convex star-shaped polyhedra. arXiv:0704.2901"},{"issue":"19","key":"9077_CR16","first-page":"75","volume":"15","author":"Yu.A. Volkov","year":"1960","unstructured":"Volkov, Yu.A.: Existence of convex polyhedra with prescribed development I. Vestn. Leningr. Univ. 15(19), 75\u201386 (1960)","journal-title":"Vestn. Leningr. Univ."},{"key":"9077_CR17","first-page":"44","volume":"5\u20136","author":"Yu.A. Volkov","year":"1968","unstructured":"Volkov, Yu.A.: An estimate for the deformation of a convex surface in dependence on the variation of its intrinsic metric. Ukr. Geom. Sb. 5\u20136, 44\u201369 (1968)","journal-title":"Ukr. Geom. Sb."},{"issue":"3\u201354","key":"9077_CR18","first-page":"83","volume":"85","author":"Yu.A. Volkov","year":"1971","unstructured":"Volkov, Yu.A., Podgornova, E.G.: Existence of a convex polyhedron with prescribed development. Ta\u0161k. Gos. Pedagog. Inst. U\u010d. Zap. 85(3\u201354), 83 (1971) (Russian)","journal-title":"Ta\u0161k. Gos. Pedagog. Inst. U\u010d. Zap."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9077-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-008-9077-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-008-9077-7","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T23:47:35Z","timestamp":1559087255000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-008-9077-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,8,19]]},"references-count":18,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2008,12]]}},"alternative-id":["9077"],"URL":"https:\/\/doi.org\/10.1007\/s00454-008-9077-7","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,8,19]]}}}