Metric Ricci curvature for $PL$ manifolds

TL;DR

This paper introduces a metric-based Ricci curvature for piecewise linear manifolds, explores its convergence, and establishes a version of the Bonnet-Myers Theorem applicable to surfaces and higher-dimensional manifolds.

Contribution

It defines a new metric Ricci curvature for PL manifolds, analyzes its convergence, and proves a generalized Bonnet-Myers Theorem for these spaces.

Findings

Defined a metric Ricci curvature for PL manifolds

Proved convergence properties of the curvature

Established a Bonnet-Myers type theorem for PL manifolds

Abstract

We introduce a metric notion of Ricci curvature for $PL$ manifolds and study its convergence properties. We also prove a fitting version of the Bonnet-Myers Theorem, for surfaces as well as for a large class of higher dimensional manifolds.