Existence, Uniqueness and Removable Singularities for Nonlinear Partial Differential Equations in Geometry

TL;DR

This paper reviews recent advances in the mathematical analysis of fully nonlinear partial differential equations on manifolds, focusing on existence, uniqueness, and removable singularities, along with related restriction theorems and principles.

Contribution

It provides a comprehensive survey of recent results on nonlinear PDEs in geometry, highlighting new developments in existence, uniqueness, and singularity removal techniques.

Findings

Summarizes recent existence and uniqueness theorems for nonlinear PDEs.

Discusses conditions for removable singularities in geometric PDEs.

Explores the application of restriction theorems and Bellman principles in this context.

Abstract

This paper surveys some recent results on existence, uniqueness and removable singularities for fully nonlinear differential equations on manifolds. The discussion also treats restriction theorems and the strong Bellman principle.