Mass functions of a compact manifold
| Autor: | Emmanuel Humbert, Andreas Hermann |
|---|---|
| Přispěvatelé: | Laboratoire de Mathématiques et Physique Théorique (LMPT), Université de Tours-Centre National de la Recherche Scientifique (CNRS), Universität Potsdam, Institut Denis Poisson (IDP), Centre National de la Recherche Scientifique (CNRS)-Université de Tours-Université d'Orléans (UO), Université de Tours (UT)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Tours (UT)-Université d'Orléans (UO) |
| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Mathematics - Differential Geometry
010102 general mathematics Institut für Mathematik General Physics and Astronomy Conformal map 01 natural sciences Infimum and supremum Combinatorics Differential Geometry (math.DG) [MATH.MATH-DG]Mathematics [math]/Differential Geometry [math.DG] 0103 physical sciences FOS: Mathematics 010307 mathematical physics Geometry and Topology Ball (mathematics) Mathematics::Differential Geometry 0101 mathematics Well-defined ddc:510 Laplace operator Mathematical Physics Mathematics Yamabe invariant |
| Popis: | Let M be a compact manifold of dimension n . In this paper, we introduce the Mass Function a ≥ 0 ↦ X + M ( a ) (resp. a ≥ 0 ↦ X − M ( a ) ) which is defined as the supremum (resp. infimum) of the masses of all metrics on M whose Yamabe constant is larger than a and which are flat on a ball of radius 1 and centered at a point p ∈ M . Here, the mass of a metric flat around p is the constant term in the expansion of the Green function of the conformal Laplacian at p . We show that these functions are well defined and have many properties which allow to obtain applications to the Yamabe invariant (i.e. the supremum of Yamabe constants over the set of all metrics on M ). |
| Databáze: | OpenAIRE |
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