Steiner and Schwarz symmetrization in warped products and fiber bundles with density

TL;DR

This paper develops broad symmetrization theorems applicable to various geometric structures like warped products and fiber bundles with density, extending classical symmetrization methods to more general settings.

Contribution

It introduces general symmetrization theorems for arbitrary dimensions and codimensions in complex geometric structures, including products, warped products, and fiber bundles with density.

Findings

General symmetrization theorems for products and fiber bundles

Extension of Steiner, Schwarz, and spherical symmetrization methods

Applicability to structures with density

Abstract

We provide very general symmetrization theorems in arbitrary dimension and codimension, in products, warped products, and certain fiber bundles such as lens spaces, including Steiner, Schwarz, and spherical symmetrization and admitting density.