Helicoidal graphs with prescribed mean curvature

TL;DR

This paper proves the existence of helicoidal graphs with a specified mean curvature in a broad class of warped product spaces, including space forms, expanding understanding of geometric structures with prescribed curvature.

Contribution

It introduces an existence theorem for helicoidal graphs with prescribed mean curvature in warped product spaces, generalizing previous results to a wider class of geometries.

Findings

Existence of helicoidal graphs with prescribed mean curvature established.

Results apply to a large class of warped product spaces including space forms.

Provides a framework for constructing such graphs in various geometric settings.

Abstract

We prove an existence result for helicoidal graphs with prescribed mean curvature in a large class of warped product spaces which comprises space forms.