Two dimensional axisymmetric smooth lattice Ricci flow

TL;DR

This paper introduces a lattice-based numerical method for Ricci flow, specifically applied to 2D axially symmetric manifolds, demonstrating its effectiveness and agreement with existing finite difference approaches.

Contribution

It presents a novel lattice method for Ricci flow in 2D axially symmetric cases, expanding computational tools for geometric analysis.

Findings

Method works well for 2D axially symmetric Ricci flow

Results agree with finite difference methods

Demonstrates effectiveness of lattice approach in geometric evolution

Abstract

A lattice based method will be presented for numerical investigations of Ricci flow. The method will be applied to the particular case of 2-dimensional axially symmetric initial data on manifolds with S^2 topology. Results will be presented that show that the method works well and agrees with results obtained using contemporary finite difference methods.