# Bianchi-convex sets and a new maximum principle for the Ricci flow

## TL;DR

This paper introduces Bianchi-convex sets, a new class of sets inspired by the second Bianchi identity, and extends Hamilton's maximum principle for the Ricci flow to these sets.

## Contribution

The paper defines Bianchi-convex sets and generalizes Hamilton's maximum principle for the Ricci flow to include these sets.

## Key findings

- Bianchi-convex sets generalize convex sets of algebraic curvature tensors.
- Hamilton's maximum principle is extended to Bianchi-convex sets.
- The new maximum principle broadens the applicability of Ricci flow analysis.

## Abstract

We introduce the new notion of Bianchi-convex sets, a generalization of convex sets of algebraic curvature tensors inspired by the second Bianchi identity. It turns out that Hamilton's maximum principle for the Ricci flow can be generalized for Bianchi-convex sets.