Heat equation and Poisson equation in matrix geometry

2013/11/21 by Jiaojiao Li, Li, Jiaojiao · 2 citations
Mathematics · Physics and Astronomy · #Geometric Analysis and Curvature Flows #Advanced Differential Geometry Research #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1311.6341

Abstract

In this paper, we study the Poisson equation and heat equation in a model matrix geometry M_n. Our main results are about the Poisson equation and global behavior of the heat equation on M_n. We can show that if c₀ is the initial positive definite matrix in M_n, then c(t) exists for all time and is positive definite too. We can also show the entropy stability of the solutions to the heat equation.

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• Noncommutative Laplacian and numerical approximation of Laplace-Beltrami spectrum of compact Riemann surfaces
• L2 norm preserving flow in matrix geometry

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