On the restriction of various Laplace operators on submanifolds

2024/05/19 by Jukka Tuomela, Tuomela, Jukka
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2405.11562

openalex publication_date 2024/05/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When considering Navier-Stokes equations on Riemannian manifolds one frequently encounters situations where the manifold is embedded in the ambient Euclidean space. In this context it is interesting to investigate what is the precise relationship of the diffusion operator in the ambient space to the diffusion operator on the manifold. The present paper gives a precise characterization of this situation for general surfaces in three dimensional space.

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