A mean curvature estimate for cylindrically bounded submanifolds

TL;DR

This paper generalizes a mean curvature estimate for cylindrically bounded submanifolds from Euclidean product spaces to more general warped product ambient spaces, broadening the applicability of such geometric bounds.

Contribution

It extends existing mean curvature estimates to submanifolds in warped product spaces, enhancing understanding of their geometric properties.

Findings

Generalized mean curvature bounds to warped product ambient spaces

Extended previous Euclidean-based estimates to broader geometric contexts

Provided new tools for analyzing submanifolds in complex ambient geometries

Abstract

We extend the estimate obtained in [1] for the mean curvature of a cylindrically bounded proper submanifold in a product manifold with an Euclidean space as one factor to a general product ambient space endowed with a warped product structure.