Relative Yamabe Invariant

2000/08/17 by Kazuo Akutagawa, Akutagawa, Kazuo, Boris Botvinnik +1 · 1 citation
Mathematics · #57R15 53C07 #Algebraic Topology (math.AT) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Spectral Theory in Mathematical Physics #math.AT #math.DG #math.GT #msc:53C07 #msc:57R15

paper · pdf · doi:10.48550/arxiv.math/0008138

24 pages, 5 fig

arxiv created 2000/08/17 · openalex publication_date 2000/08/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We define a relative Yamabe invariant of a smooth manifold with given conformal class on its boundary. In the case of empty boundary the invariant coincides with the classic Yamabe invariant. We develop approximation technique which leads to gluing theorems of two manifolds along their boundaries for the relative Yamabe invariant. We show that there are many examples of manifolds with both positive and non-positive relative Yamabe invariants.

Cited by

• The space of metrics with positive generalized conformal Laplacian

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