A geometric maximum principle, plateau’s problem for surfaces of prescribed mean curvature, and the two dimensional analogue of the catenary

1988 ◽  
pp. 116-141 ◽  
Author(s):  
Ulrich Dierkes
Keyword(s):  
Maximum Principle ◽  
Mean Curvature ◽  
Two Dimensional ◽  
Plateau’S Problem ◽  
Prescribed Mean Curvature ◽  
Plateau's Problem

scholarly journals Potential theory for manifolds with boundary and applications to controlled mean curvature graphs

2017 ◽  
Vol 2017 (733) ◽  
Author(s):  
Debora Impera ◽  
Stefano Pigola ◽  
Alberto G. Setti
Keyword(s):  
Maximum Principle ◽  
Potential Theory ◽  
Mean Curvature ◽  
Manifolds With Boundary ◽  
Riemannian Product ◽  
Prescribed Mean Curvature ◽  
New Information ◽  
New Form

AbstractIn this paper we characterize the Neumann-parabolicity of manifolds with boundary in terms of a new form of the classical Ahlfors maximum principle and of a version of the so-called Kelvin–Nevanlinna–Royden criterion. The motivation underlying this study is to obtain new information on the geometry of graphs with prescribed mean curvature inside a Riemannian product of the type

scholarly journals Hölder regularity at the boundary of two-dimensional sliding almost minimal sets

2018 ◽  
Vol 11 (1) ◽  
pp. 29-63
Author(s):  
Yangqin Fang
Keyword(s):  
Regularity Result ◽  
Hölder Regularity ◽  
Two Dimensional ◽  
Soap Films ◽  
Regularity Theorem ◽  
Plateau’S Problem ◽  
Minimal Sets ◽  
Plateau's Problem ◽  
Dimension 2 ◽  
Holder Regularity

AbstractIn [15], Jean Taylor proved a regularity theorem away from the boundary for Almgren almost minimal sets of dimension 2 in {\mathbb{R}^{3}}. It is quite important for understanding the soap films and the solutions of Plateau’s problem away from boundary. In this paper, we will give a regularity result on the boundary for two-dimensional sliding almost minimal sets in {\mathbb{R}^{3}}.

scholarly journals A Note on the Strong Maximum Principle for Fully Nonlinear Equations on Riemannian Manifolds

2021 ◽  
Author(s):  
Alessandro Goffi ◽  
Francesco Pediconi
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Strong Maximum Principle ◽  
Second Order ◽  
Fully Nonlinear Equations ◽  
Nonlinear Operators ◽  
Fully Nonlinear ◽  
Second Order Equations ◽  
Curvature Type

AbstractWe investigate strong maximum (and minimum) principles for fully nonlinear second-order equations on Riemannian manifolds that are non-totally degenerate and satisfy appropriate scaling conditions. Our results apply to a large class of nonlinear operators, among which Pucci’s extremal operators, some singular operators such as those modeled on the p- and $$\infty $$ ∞ -Laplacian, and mean curvature-type problems. As a byproduct, we establish new strong comparison principles for some second-order uniformly elliptic problems when the manifold has nonnegative sectional curvature.

Sign in / Sign up

Export Citation Format

Share Document