# On compact Riemannian manifolds with convex boundary and Ricci curvature bounded from below

## TL;DR

This paper introduces a new approach to studying compact Riemannian manifolds with convex boundaries under Ricci curvature constraints, formulates conjectures, and provides partial results supporting them.

## Contribution

It presents a novel methodology for analyzing such manifolds, formulates new conjectures, and offers partial theoretical support for these conjectures.

## Key findings

- Formulation of new conjectures regarding Ricci curvature and convex boundaries.
- Partial results supporting the proposed conjectures.
- Development of a new analytical approach for these manifolds.

## Abstract

We propose a new approach to the study of compact Riemannian manifolds with nonnegative Ricci curvature and strictly convex boundary or positive Ricci curvature and convex boundary. Several conjectures are formulated. Some partial results that support these conjectures are established.