The Dirichlet problem for Hessian equations on Riemannian manifolds

1999 ◽  
Vol 8 (1) ◽  
pp. 45-69 ◽  
Author(s):  
Bo Guan
Keyword(s):  
Dirichlet Problem ◽  
Riemannian Manifolds ◽  
Hessian Equations

scholarly journals Torsional rigidity on compact Riemannian manifolds with lower Ricci curvature bounds

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Najoua Gamara ◽  
Abdelhalim Hasnaoui ◽  
Akrem Makni
Keyword(s):  
Riemannian Manifold ◽  
Dirichlet Problem ◽  
Ricci Curvature ◽  
Riemannian Manifolds ◽  
Compact Riemannian Manifold ◽  
Torsional Rigidity ◽  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Curvature Bounds ◽  
Reverse Hölder

AbstractIn this article we prove a reverse Hölder inequality for the fundamental eigenfunction of the Dirichlet problem on domains of a compact Riemannian manifold with lower Ricci curvature bounds. We also prove an isoperimetric inequality for the torsional ridigity of such domains

The Dirichlet Problem for Degenerate Hessian Equations

2005 ◽  
Vol 29 (1-2) ◽  
pp. 219-235 ◽  
Author(s):  
Nina Ivochkina ◽  
Neil Trudinger ◽  
Xu-Jia Wang
Keyword(s):  
Dirichlet Problem ◽  
Hessian Equations

scholarly journals On the exterior Dirichlet problem for Hessian equations

2014 ◽  
Vol 366 (12) ◽  
pp. 6183-6200 ◽  
Author(s):  
Jiguang Bao ◽  
Haigang Li ◽  
Yanyan Li
Keyword(s):  
Dirichlet Problem ◽  
Hessian Equations

scholarly journals The Degenerate Special Lagrangian Equation on Riemannian Manifolds

2018 ◽  
Vol 2020 (9) ◽  
pp. 2832-2863
Author(s):  
Matthew Dellatorre
Keyword(s):  
Riemannian Manifold ◽  
Dirichlet Problem ◽  
Riemannian Manifolds ◽  
Duality Theory ◽  
Continuous Solutions ◽  
Lagrangian Equation ◽  
Base Manifold ◽  
Special Lagrangian ◽  
Euclidean Setting ◽  
Special Lagrangian Equation

Abstract We show that the degenerate special Lagrangian equation (DSL), recently introduced by Rubinstein–Solomon, induces a global equation on every Riemannian manifold, and that for certain associated geometries this equation governs, as it does in the Euclidean setting, geodesics in the space of positive Lagrangians. For example, geodesics in the space of positive Lagrangian sections of a smooth Calabi–Yau torus fibration are governed by the Riemannian DSL on the base manifold. We then develop their analytic techniques, specifically modifications of the Dirichlet duality theory of Harvey–Lawson, in the Riemannian setting to obtain continuous solutions to the Dirichlet problem for the Riemannian DSL and hence continuous geodesics in the space of positive Lagrangians.

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