Regularity of $$C^1$$ C 1 surfaces with prescribed mean curvature in three-dimensional contact sub-Riemannian manifolds

2015 ◽  
Vol 54 (3) ◽  
pp. 2503-2516 ◽  
Author(s):  
Matteo Galli ◽  
Manuel Ritoré
Keyword(s):  
Riemannian Manifolds ◽  
Mean Curvature ◽  
Three Dimensional ◽  
Prescribed Mean Curvature

On the Prescribed Scalar and Zero Mean Curvature on 3-Dimensional Manifolds With Umbilic Boundary

2006 ◽  
Vol 6 (1) ◽  
Author(s):  
Mohameden Ould Ahmedou
Keyword(s):  
Mean Curvature ◽  
Three Dimensional ◽  
Riemannian Metrics ◽  
Dimensional Manifold ◽  
3 Dimensional ◽  
Prescribed Mean Curvature ◽  
Zero Mean Curvature ◽  
Boundary Mean Curvature

AbstractIn this paper we consider the existence and the compactness of Riemannian metrics of prescribed mean curvature and zero boundary mean curvature on a three dimensional manifold with umbilic boundary (M, g

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.

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