A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary

Alessandro Carlotto; Chao Li

doi:10.3842/SIGMA.2024.014

A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary

Alessandro Carlotto, Chao Li

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain spaces of metrics defined by a suitable spectral “stability” condition. We develop some basic tools and obtain a rather complete picture in the case of surfaces.

Original language	English (US)
Article number	014
Journal	Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Volume	20
DOIs	https://doi.org/10.3842/SIGMA.2024.014
State	Published - 2024

Keywords

concordance
free boundary minimal surfaces
isotopy
positive scalar curvature

ASJC Scopus subject areas

Analysis
Mathematical Physics
Geometry and Topology

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10.3842/SIGMA.2024.014

Cite this

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abstract = "We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain spaces of metrics defined by a suitable spectral “stability” condition. We develop some basic tools and obtain a rather complete picture in the case of surfaces.",

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author = "Alessandro Carlotto and Chao Li",

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AU - Li, Chao

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AB - We study notions of isotopy and concordance for Riemannian metrics on manifolds with boundary and, in particular, we introduce two variants of the concept of minimal concordance, the weaker one naturally arising when considering certain spaces of metrics defined by a suitable spectral “stability” condition. We develop some basic tools and obtain a rather complete picture in the case of surfaces.

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KW - isotopy

KW - positive scalar curvature

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A Note about Isotopy and Concordance of Positive Scalar Curvature Metrics on Compact Manifolds with Boundary

Abstract

Keywords

ASJC Scopus subject areas

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