The Yamabe equation in small convex domains in $\mathbb{R}^3$ and small balls in $\mathbb{R}^n$

TL;DR

This paper introduces an iterative method to solve a Yamabe-type equation with Dirichlet boundary conditions in small convex domains and balls in three-dimensional space, advancing the understanding of geometric PDEs in constrained regions.

Contribution

The paper presents a novel iterative approach for solving Yamabe-type equations specifically in small convex domains and small balls in b4b3, expanding solution techniques for geometric PDEs.

Findings

Successful implementation of the iterative method in small convex domains.

Effective solution of Yamabe-type equations in small balls in b4b3.

Potential for extending methods to other geometric PDEs.

Abstract

We show an iterative method to solve a Dirichlet problem for a Yamabe-type equation in small convex domains in $\mathbb{R}^3$ and small balls in $\mathbb{R}^3$.