A remark on compact H-surfaces into R^3

TL;DR

This paper demonstrates the existence of solutions to the H-system on an annulus with Neumann boundary conditions using a functional related to the optimal Wente inequality, contributing to geometric analysis.

Contribution

It introduces a new approach leveraging the Wente inequality to establish solutions for the H-system with specific boundary conditions.

Findings

Existence of solutions to the H-system on an annulus.

Application of the Wente inequality in geometric PDEs.

Solutions satisfy Neumann boundary conditions.

Abstract

Using the functional associated with the optimal Wente inequality for pairs of functions on 2-dimensional domains, we show the existence of solutions to the H-system on an annulus satisfying Neumann boundary conditions.