{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,27]],"date-time":"2026-03-27T07:26:42Z","timestamp":1774596402937,"version":"3.50.1"},"reference-count":23,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2007,9,11]],"date-time":"2007-09-11T00:00:00Z","timestamp":1189468800000},"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":[[2007,12]]},"DOI":"10.1007\/s00454-007-9009-y","type":"journal-article","created":{"date-parts":[[2007,9,10]],"date-time":"2007-09-10T10:29:09Z","timestamp":1189420149000},"page":"651-664","source":"Crossref","is-referenced-by-count":17,"title":["A Monotonicity Property for Weighted Delaunay Triangulations"],"prefix":"10.1007","volume":"38","author":[{"given":"David","family":"Glickenstein","sequence":"first","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2007,9,11]]},"reference":[{"key":"9009_CR1","series-title":"Handbook of Computational Geometry","first-page":"201","volume-title":"Voronoi Diagrams","author":"F. Aurenhammer","year":"2000","unstructured":"Aurenhammer, F., Klein, R.: Voronoi Diagrams. Handbook of Computational Geometry, pp.\u00a0201\u2013290. North-Holland, Amsterdam (2000)"},{"key":"9009_CR2","unstructured":"Bobenko, A.I., Springborn, B.A.: A discrete Laplace-Beltrami operator for simplicial surfaces. ArXiv: math.DG\/0503219 (2005)"},{"key":"9009_CR3","doi-asserted-by":"crossref","first-page":"97","DOI":"10.4310\/jdg\/1080835659","volume":"63","author":"B. Chow","year":"2003","unstructured":"Chow, B., Luo, F.: Combinatorial Ricci flows on surfaces. J. Differ. Geom. 63, 97\u2013129 (2003)","journal-title":"J. Differ. Geom."},{"key":"9009_CR4","series-title":"CBMS Regional Conference Series in Mathematics","volume-title":"Spectral Graph Theory","author":"F.R.K. Chung","year":"1997","unstructured":"Chung, F.R.K.: Spectral Graph Theory. CBMS Regional Conference Series in Mathematics, vol.\u00a092. American Mathematical Society, Providence (1997)"},{"key":"9009_CR5","unstructured":"Coolidge, J.L.: A treatise on the circle and the sphere. Reprint of the 1916 edition. Chelsea Publishing Co., Bronx, NY (1971)"},{"issue":"1","key":"9009_CR6","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1007\/PL00009447","volume":"22","author":"T. Dubejko","year":"1999","unstructured":"Dubejko, T.: Discrete solutions of Dirichlet problems, finite volumes, and circle packings. Discrete Comput. Geom. 22(1), 19\u201339 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"9009_CR7","first-page":"793","volume":"8","author":"R.J. Duffin","year":"1959","unstructured":"Duffin, R.J.: Distributed and lumped networks. J. Math. Mech. 8, 793\u2013826 (1959)","journal-title":"J. Math. Mech."},{"key":"9009_CR8","doi-asserted-by":"crossref","unstructured":"Edelsbrunner, H.: Triangulations and meshes in computational geometry. Acta Numer. 133\u2013213, (2000)","DOI":"10.1017\/S0962492900001331"},{"issue":"3","key":"9009_CR9","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1007\/BF01975867","volume":"15","author":"H. Edelsbrunner","year":"1996","unstructured":"Edelsbrunner, H., Shah, N.R.: Incremental topological flipping works for regular triangulations. Algorithmica 15(3), 223\u2013241 (1996)","journal-title":"Algorithmica"},{"key":"9009_CR10","series-title":"Mathematics: Theory & Applications","doi-asserted-by":"crossref","DOI":"10.1007\/978-0-8176-4771-1","volume-title":"Discriminants, Resultants, and Multidimensional Determinants","author":"I.M. Gelfand","year":"1994","unstructured":"Gelfand, I.M., Kapranov, M.M., Zelevinsky, A.V.: Discriminants, Resultants, and Multidimensional Determinants. Mathematics: Theory & Applications. Birkh\u00e4user Boston, Boston (1994)"},{"issue":"4","key":"9009_CR11","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1016\/j.top.2005.02.001","volume":"44","author":"D. Glickenstein","year":"2005","unstructured":"Glickenstein, D.: A combinatorial Yamabe flow in three dimensions. Topology 44(4), 791\u2013808 (2005)","journal-title":"Topology"},{"issue":"4","key":"9009_CR12","doi-asserted-by":"crossref","first-page":"809","DOI":"10.1016\/j.top.2005.02.002","volume":"44","author":"D. Glickenstein","year":"2005","unstructured":"Glickenstein, D.: A maximum principle for combinatorial Yamabe flow. Topology 44(4), 809\u2013825 (2005)","journal-title":"Topology"},{"key":"9009_CR13","unstructured":"Glickenstein, D.: Geometric triangulations and discrete Laplacians. ArXiv: math.MG\/0508188 (2005)"},{"key":"9009_CR14","unstructured":"Hirani, A.N.: Discrete exterior calculus. Ph.D. thesis, California Institute of Technology, Pasadena, CA (May 2003)"},{"issue":"1\u20132","key":"9009_CR15","doi-asserted-by":"crossref","first-page":"263","DOI":"10.1016\/S0304-3975(00)00248-6","volume":"263","author":"C. Indermitte","year":"2001","unstructured":"Indermitte, C., Liebling, T.M., Troyanov, M., Cl\u00e9men\u00e7on, H.: Voronoi diagrams on piecewise flat surfaces and an application to biological growth. Theor. Comput. Sci. 263(1\u20132), 263\u2013274 (2001)","journal-title":"Theor. Comput. Sci."},{"key":"9009_CR16","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/B978-0-12-587260-7.50011-X","volume-title":"Mathematical Software III","author":"C.L. Lawson","year":"1977","unstructured":"Lawson, C.L.: Software for C 1 surface interpolation. In: Mathematical Software III, pp. 161\u2013194. Academic Press, New York (1977)"},{"issue":"5","key":"9009_CR17","doi-asserted-by":"crossref","first-page":"765","DOI":"10.1142\/S0219199704001501","volume":"6","author":"F. Luo","year":"2004","unstructured":"Luo, F.: Combinatorial Yamabe flow on surfaces. Commun. Contemp. Math. 6(5), 765\u2013780 (2004)","journal-title":"Commun. Contemp. Math."},{"key":"9009_CR18","doi-asserted-by":"crossref","first-page":"35","DOI":"10.1007\/978-3-662-05105-4_2","volume-title":"Visualization and Mathematics III, Math. Vis.","author":"M. Meyer","year":"2003","unstructured":"Meyer, M., Desbrun, M., Schr\u00f6der, P., Barr, A.H.: Discrete differential geometry operators for triangulated 2-manifolds. In: Visualization and Mathematics III, Math. Vis., pp. 35\u201357. Springer, Berlin (2003)"},{"key":"9009_CR19","volume-title":"Geometry, a Comprehensive Course","author":"D. Pedoe","year":"1988","unstructured":"Pedoe, D.: Geometry, a Comprehensive Course, 2nd edn. Dover, New York (1988)","edition":"2"},{"issue":"1","key":"9009_CR20","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1080\/10586458.1993.10504266","volume":"2","author":"U. Pinkall","year":"1993","unstructured":"Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Exp. Math. 2(1), 15\u201336 (1993)","journal-title":"Exp. Math."},{"issue":"6","key":"9009_CR21","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1016\/0167-8396(92)90047-S","volume":"9","author":"P.L. Powar","year":"1992","unstructured":"Powar, P.L.: Minimal roughness property of the Delaunay triangulation: a shorter approach. Comput. Aided Geom. Des. 9(6), 491\u2013494 (1992)","journal-title":"Comput. Aided Geom. Des."},{"key":"9009_CR22","doi-asserted-by":"crossref","first-page":"489","DOI":"10.1016\/0167-8396(90)90011-F","volume":"7","author":"S. Rippa","year":"1990","unstructured":"Rippa, S.: Minimal roughness property of the Delaunay triangulation. Comput. Aided Geom. Des. 7, 489\u2013497 (1990)","journal-title":"Comput. Aided Geom. Des."},{"issue":"3","key":"9009_CR23","doi-asserted-by":"crossref","first-page":"553","DOI":"10.2307\/2118572","volume":"139","author":"I. Rivin","year":"1994","unstructured":"Rivin, I.: Euclidean structures on simplicial surfaces and hyperbolic volume. Ann. Math. (2) 139(3), 553\u2013580 (1994)","journal-title":"Ann. Math. (2)"}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-007-9009-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-007-9009-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-007-9009-y","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T19:47:33Z","timestamp":1559072853000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-007-9009-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,9,11]]},"references-count":23,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2007,12]]}},"alternative-id":["9009"],"URL":"https:\/\/doi.org\/10.1007\/s00454-007-9009-y","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2007,9,11]]}}}