An integral equation in conformal geometry
Fengbo Hang, Xiaodong Wang, Xiaodong Yan
Abstract
We study the existence of a metric with zero scalar curvature maximizing the isoperimetric ratio among all zero scalar curvature metrics in a fixed conformal class of metrics on a compact manifold with boundary. The question may be reduced to an extremal problem for the harmonic extension of functions and the related nonlinear integral equation is discussed.
Create a lesson
Related papers
Global existence of smooth solutions to the Navier-Stokes equations for initial data with infinite energy
Alexey Cheskidov, Hedong Hou
Sharp Global Well-Posedness for the Logarithmically Regularized 2D Euler Equations
Zachary Radke
Optimal transport to non-convex polyhedral domains
Shibing Chen, Qi-Rui Li, Yuanyuan Li et al.
Generalized minimizers for the capillarity energy outside convex obstacles
Gabriele Nani, Simone Vincini
Generic boundary behavior of Dirichlet eigenfunctions
Alec Payne, Zihui Zhao
Near-boundary rigidity and strict maximum modulus for Neumann eigenfunctions on convex planar domains
Haiyun Deng, Xuyong Jiang, Xiaoping Yang