# Nearly optimal stability for Serrin's problem and the Soap Bubble theorem

## TL;DR

This paper provides improved quantitative estimates for classical geometric problems like Serrin's overdetermined problem and Alexandrov's Soap Bubble Theorem, achieving near-optimal results and advancing understanding of symmetry and stability in these contexts.

## Contribution

The authors introduce new, sharper estimates for stability in Serrin's problem and the Soap Bubble Theorem, improving previous results and in some cases reaching optimality.

## Key findings

- Enhanced stability estimates for Serrin's problem.
- Improved bounds for Alexandrov's Soap Bubble Theorem.
- Some estimates are proven to be optimal.

## Abstract

We present new quantitative estimates for the radially symmetric configuration concerning Serrin's overdetermined problem for the torsional rigidity, Alexandrov's Soap Bubble Theorem, and other related problems. The new estimates improve on those obtained in two our previous articles, and are in some cases optimal.