%0 Journal Article %1 citeulike:7355261 %A Finn, Robert %A McCuan, John %C Mathematics Department, Stanford University, Stanford, CA 94305-2125, USA; Mathematics Departement, University of California, Berkeley, Berkeley, CA 94720, USA %D 2000 %J Mathematische Nachrichten %K 76b45-capillarity 53a10-minimal-surfaces-surfaces-with-prescribed-mean-curvature 49q05-calculus-of-variations-minimal-surfaces %N 1 %P 115--135 %R 10.1002/(sici)1522-2616(200001)209:1\%3C115::aid-mana115\%3E3.0.co;2-j %T Vertex Theorems for Capillary Drops on Support Planes %U http://dx.doi.org/10.1002/(sici)1522-2616(200001)209:1\%3C115::aid-mana115\%3E3.0.co;2-j %V 209 %X We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results extend the classical theorem of H. Hopf on constant mean curvature immersions of the sphere. The conclusion of sphericity cannot be extended to more than three vertices, as we show by examples.

@article{citeulike:7355261, abstract = {{We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results extend the classical theorem of H. Hopf on constant mean curvature immersions of the sphere. The conclusion of sphericity cannot be extended to more than three vertices, as we show by examples.}}, added-at = {2017-06-29T07:13:07.000+0200}, address = {Mathematics Department, Stanford University, Stanford, CA 94305-2125, USA; Mathematics Departement, University of California, Berkeley, Berkeley, CA 94720, USA}, author = {Finn, Robert and McCuan, John}, biburl = {https://www.bibsonomy.org/bibtex/29fd0ce55e9a55fe71eafafbf9c1c9b49/gdmcbain}, citeulike-article-id = {7355261}, citeulike-attachment-1 = {finn_00_vertex_508217.pdf; /pdf/user/gdmcbain/article/7355261/508217/finn_00_vertex_508217.pdf; b4221253d11d692b9d9adc8eaaea9db77cf6f26e}, citeulike-linkout-0 = {http://dx.doi.org/10.1002/(sici)1522-2616(200001)209:1\%3C115::aid-mana115\%3E3.0.co;2-j}, citeulike-linkout-1 = {http://www3.interscience.wiley.com/cgi-bin/abstract/72000414/ABSTRACT}, doi = {10.1002/(sici)1522-2616(200001)209:1\%3C115::aid-mana115\%3E3.0.co;2-j}, file = {finn_00_vertex_508217.pdf}, interhash = {2047a23bd5599af380edc52bf5b178ad}, intrahash = {9fd0ce55e9a55fe71eafafbf9c1c9b49}, issn = {1522-2616}, journal = {Mathematische Nachrichten}, keywords = {76b45-capillarity 53a10-minimal-surfaces-surfaces-with-prescribed-mean-curvature 49q05-calculus-of-variations-minimal-surfaces}, number = 1, pages = {115--135}, posted-at = {2010-06-24 01:29:07}, priority = {2}, timestamp = {2021-10-14T06:38:49.000+0200}, title = {{Vertex Theorems for Capillary Drops on Support Planes}}, url = {http://dx.doi.org/10.1002/(sici)1522-2616(200001)209:1\%3C115::aid-mana115\%3E3.0.co;2-j}, volume = 209, year = 2000 }