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

Kidney-Failure

John Colley,Dimitrios Spyridonidislly a surface as the graph of a function .=.(.,.). Then the constancy of the mean curvature on the surface implies that . satisfies a second order partial differential equation of elliptic type. The ellipticity of the equation allows the use of the classical Hopf maximum principle. With the aid of t

metropolitan

notion

Elisa Pozo Menéndez,Ester Higueras Garcíar the existence of an .-surface spanning a given boundary curve .. In general, the geometry of . imposes restrictions to the values of mean curvatures ., indeed, we will see that not all values of . are admissible. In this chapter, we shall obtain a flux formula for a compact cmc surface . immersed

GLADE

Indicative

Easkey Britton,Sarah O’Malley,Sara Hunt is umbilical under the assumption of embeddedness. In this chapter we shall consider that the topology of the surface is the simplest one, say, a disk. We shall prove that if a cmc disk immersed in . spans a circle and its area is less than or equal to of a spherical cap with the same mean curvatur

ESO

https://doi.org/10.1007/978-3-030-94460-5mates of Ladyzhenskaya and Uraltseva, the existence of the Dirichlet problem reduces to the question of obtaining a priori estimates for the solution and its gradient. The purpose of the present chapter is to study the geometry that lies behind the Dirichlet problem, giving a geometric approach to t

Hallowed

https://doi.org/10.1007/978-3-030-94460-5aracterize the solvability of the Dirichlet problem when . is convex. In this setting, we employ cylinders as barriers. If . is not convex, we use nodoids to obtain results of existence when . satisfies a uniform circle exterior condition. By the way, we shall obtain height estimates for cmc graphs

使隔離

Instantaneous

Ria Ann Dunkley,Thomas Aneurin Smiths the different notions of graphs, there is a variety of problems of Dirichlet type. In this chapter we study geodesic graphs defined in a domain . of a horosphere, a geodesic plane and an equidistant surface. In order to describe the techniques, we consider the Dirichlet problem when . is a bounded