scholarly journals A Geometric Maximum Principle for Surfaces of Prescribed Mean Curvature in Riemannian Manifolds

1989 ◽  
Vol 8 (2) ◽  
pp. 97-102 ◽  
Author(s):  
Ulrich Dierkes
Keyword(s):  
Maximum Principle ◽  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Prescribed Mean Curvature

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.

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

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