Unified $(\alpha,\beta)$-Flows on Triangulated Manifolds with Two and Three Dimensions

TL;DR

This paper introduces a unified framework for $(eta,eta)$-flows on 2D and 3D triangulated manifolds, consolidating various existing discrete curvature flows into a single comprehensive approach.

Contribution

It presents a novel unified $(eta,eta)$-flow framework that encompasses multiple prior discrete curvature flows on triangulated manifolds.

Findings

Unified framework simplifies analysis of discrete curvature flows.

Connects various existing flows under a common theoretical structure.

Facilitates new insights into geometric properties of triangulated manifolds.

Abstract

In this paper, we introduce a framework of $(\alpha,\beta)$-flows on triangulated manifolds with two and three dimensions, which unifies several discrete curvature flows previously defined in the literature.