Titlebook: Constant Mean Curvature Surfaces with Boundary; Rafael López Book 2013 Springer-Verlag Berlin Heidelberg 2013 53, 53A, 53A10, 53C42, 35J,

modest

官僚統(tǒng)治

Surfaces with Constant Mean Curvature,f a cmc surface. As the Laplacian operator is elliptic, the maximum principle yields height estimates of a graph of constant mean curvature. Finally, and with the aid of the expression of these Laplacians, we will derive the Barbosa-do Carmo theorem that characterizes a round sphere in the family of closed stable cmc surfaces of Euclidean space.

interference

The Dirichlet Problem in Unbounded Domains,hod of super and subsolutions. The subsolution will be a solution of the minimal surface equation, while a supersolution is replaced by a family of local upper barriers, which will be pieces of cylinders or nodoids depending on the domain.

叢林

扔掉掐死你

John Colley,Dimitrios Spyridonidist the surface lies on one side of the boundary plane. Comparing the surface with spheres and cylinders with the same mean curvature, we obtain characterizations of a sphere if the surface is included in the closure of an Euclidean ball or a cylinder whose radii are related with the value of the mean curvature of the surface.

智力高

hematuria

Elisa Pozo Menéndez,Ester Higueras García the value of mean curvature of the surface. In the last section, we will prove that if an embedded surface with convex boundary is transverse to the boundary plane then it lies on one side of this plane.

圣歌

https://doi.org/10.1007/978-3-030-94460-5ylinders, we shall assume that the domain is convex, and if we employ nodoids, we suppose that the domain satisfies a certain exterior circle condition. We finish the chapter with a discussion of the corresponding Dirichlet problem of the cmc equation in domains of the unit sphere whose solutions represent radial graphs.

冷漠

乳汁

The Comparison and Tangency Principles,t the surface lies on one side of the boundary plane. Comparing the surface with spheres and cylinders with the same mean curvature, we obtain characterizations of a sphere if the surface is included in the closure of an Euclidean ball or a cylinder whose radii are related with the value of the mean curvature of the surface.