Generalized scalar curvature type equations on compact Riemannian manifolds

1998 ◽  
Vol 327 (4) ◽  
pp. 377-381 ◽  
Author(s):  
Olivier Druet
Keyword(s):  
Scalar Curvature ◽  
Riemannian Manifolds ◽  
Curvature Type

Generalized scalar curvature type equations on compact Riemannian manifolds

2000 ◽  
Vol 130 (4) ◽  
pp. 767-788 ◽  
Author(s):  
Olivier Druet
Keyword(s):  
Scalar Curvature ◽  
Laplace Operator ◽  
Nonlinear Equations ◽  
Riemannian Manifolds ◽  
Curvature Equation ◽  
Curvature Type

The paper is concerned with nonlinear equations of critical Sobolev growth involving the p-Laplace operator. These equations generalize the more classical scalar curvature equation.

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.

Nonexistence Results of Sign-changing solutions for a Supercritical Problem of the Scalar Curvature Type

2012 ◽  
Vol 12 (1) ◽  
Author(s):  
Kamal Ould Bouh
Keyword(s):  
Critical Exponent ◽  
Scalar Curvature ◽  
Elliptic Problem ◽  
Nonlinear Elliptic Problem ◽  
Nonlinear Elliptic ◽  
Sign Changing Solutions ◽  
Supercritical Problem ◽  
Curvature Type

AbstractThis paper is devoted to the study of the nonlinear elliptic problem with supercritical critical exponent (P

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