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

被引：0

作者：

Carlotto, Alessandro ^{[1
]}

Li, Chao ^{[2
]}

机构：

[1] Univ Trento, Dipartimento Matemat, Via Sommar 14, I-38123 Trento, Italy

[2] NYU, Courant Inst Math Sci, 251 Mercer St, New York, NY 10012 USA

来源：

SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2024年 / 20卷

基金：

欧洲研究理事会;

关键词：

positive scalar curvature; isotopy; concordance; free boundary minimal surfaces;

D O I：

10.3842/SIGMA.2024.014

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页数：13

共 34 条

[1]

Agostiniani V, 2022, Arxiv, DOI arXiv:2205.11642

[2] An obstruction to the positivity of relative Yamabe invariants [J].

Akutagawa, K .

MATHEMATISCHE ZEITSCHRIFT, 2003, 243 (01) :85-98

[3] The relative Yamabe invariant [J].

Akutagawa, K ;

Botvinnik, B .

COMMUNICATIONS IN ANALYSIS AND GEOMETRY, 2002, 10 (05) :935-969

[4] Manifolds of positive scalar curvature and conformal cobordism theory [J].

Akutagawa, K ;

Botvinnik, B .

MATHEMATISCHE ANNALEN, 2002, 324 (04) :817-840

[5]

Bar C., 2023, PERSPECTIVES SCALAR, P325

[6] NEW DEFINITION OF QUASILOCAL MASS [J].

BARTNIK, R .

PHYSICAL REVIEW LETTERS, 1989, 62 (20) :2346-2348

[7]

Besse A., 1987, EINSTEIN MANIFOLDS

[8]

Besse A.L., 1978, ERGEB MATH GRENZGEB, V93

[9]

Bourguignon J. P., 1974, J.Funct. Anal, V15, P341, DOI [10.1016/0022-1236(74)90027-5, DOI 10.1016/0022-1236(74)90027-5]

[10] STABILITY AND ISOLATION PHENOMENA FOR YANG-MILLS FIELDS [J].

BOURGUIGNON, JP ;

LAWSON, HB .

COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1981, 79 (02) :189-230

← 1 2 3 4 →