Eigenvalue estimates and differential form Laplacians on Alexandrov\n spaces

2017/05/23 by John Lott, Lott, John · 1 citation
Computer Science · Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.1705.08400

openalex publication_date 2017/05/23 · openalex created_date 2022/08/24 · openalex updated_date 2026/07/28

Abstract

We give upper bounds on the eigenvalues of the differential form Laplacian on\na compact Riemannian manifold. The proof uses Alexandrov spaces with curvature\nbounded below. We also construct differential form Laplacians on Alexandrov\nspaces. Under a local biLipschitz assumption on the Alexandrov space, which is\nconjecturally always satisfied, we show that the differential form Laplacian\nhas a compact resolvent. We identify its kernel with an intersection homology\ngroup.\n

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• Small eigenvalues of the Hodge-Laplacian with sectional curvature bounded below

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