An obstruction to the positivity of relative Yamabe invariants
type: Item
instance of: scholarly article
title: An obstruction to the positivity of relative Yamabe invariants
zbMATH Open document ID: 1034.53030
author: Kazuo Akutagawa
published in: Mathematische Zeitschrift
publication date: 2003-06-02T00:00:00Z
review text: Let \(W\) be a compact manifold with nonempty boundary \(M\). The author studies the question ``does there exist a positive scalar curvature metric on \(W\) with minimal boundary condition?'' The author presents an obstruction to the existence of such a metric in terms of the geometry of the boundary \(M\) and of \(W\). This obstruction arises from combining the bordism theoretical construction of Stolz and the minimal hypersurface method of Schoen-Yau. The author uses this obstruction to present some examples of compact manifolds with nonempty boundary which do not admit a positive scalar curvature metric. The relative Yamabe invariant of Akutagawa and Botvinnik plays a central role in the discussion.
reviewed by: Peter B. Gilkey
Mathematics Subject Classification ID: 53C20
Mathematics Subject Classification ID: 53C21
Mathematics Subject Classification ID: 57R90
zbMATH DE Number: 1922487
zbMATH Keywords: positive scalar curvature
zbMATH Keywords: Stolz obstruction group
zbMATH Keywords: minimal boundary condition
zbMATH Keywords: Yamabe invariant.
MaRDI profile type: Publication
full work available at URL: s00209-002-0450-6
OpenAlex ID: W2016416213
DOI: 10.1007/S00209-002-0450-6
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description: scientific article; zbMATH DE number 1922487