Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds
Numerical Analysis
2024-09-24 v1 Numerical Analysis
Differential Geometry
Abstract
In this paper, we present a method for digitally representing the "volume element" and calculating the integral of a function on compact hypersurfaces with or without boundary, and low-dimensional submanifolds in . We also extend such calculation to hypersurfaces in compact Riemannnian manifolds.
Cite
@article{arxiv.2409.14151,
title = {Numerical calculation method for function integration on submanifolds of $\mathbb{R}^n$ or compact Riemannian manifolds},
author = {Fusheng Deng and Gang Huang and Yingyi Wu},
journal= {arXiv preprint arXiv:2409.14151},
year = {2024}
}