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- W84706687 abstract "In this chapter we address the study of the area and the volume of a compact cmc surface with boundary. We shall see how the control of the area or the volume provides information concerning the geometry of the surface. The chapter begins obtaining a monotonicity formula for the area in terms of the height of the surface and we will show that the solutions of the isoperimetric problem for a convex planar domain are graphs if the volume is sufficiently small. In the case that the volume is large, one expects that the surface looks like a large spherical cap. We will prove this fact for the case of an embedded cmc surface spanning a convex curve and the surface lies on one side of the boundary plane." @default.
- W84706687 created "2016-06-24" @default.
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- W84706687 date "2013-01-01" @default.
- W84706687 modified "2023-10-18" @default.
- W84706687 title "The Area and the Volume of a Constant Mean Curvature Surface" @default.
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- W84706687 doi "https://doi.org/10.1007/978-3-642-39626-7_6" @default.
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