On the global existence of generalized rotational hypersurfaces with prescribed mean curvature in the Euclidean spaces, II

TL;DR

This paper extends previous work by proving the existence of generalized rotational hypersurfaces with prescribed mean curvature in Euclidean spaces for all types, building on earlier specific cases.

Contribution

It generalizes the existence results of rotational hypersurfaces with prescribed mean curvature to all types, beyond the specific cases previously studied.

Findings

Existence of generalized rotational hypersurfaces with prescribed mean curvature for all types.

Extension of previous results to broader classes of hypersurfaces.

Validation of the existence through mathematical proof.

Abstract

In the previous paper, it has been proved that the generalized rotational hypersurfaces of O(n-1)-type and O (l+1) x O(m+1)-type, for which the mean curvature is any prescribed continuous function. This paper is a sequel, and a similar existence result is shown for any type.