Mass functions of a compact manifold - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2018

Mass functions of a compact manifold

Abstract

Let $M$ be a compact manifold of dimension $n$. In this paper, we introduce the {\em Mass Function} $a \geq 0 \mapsto \xp{M}{a}$ (resp. $a \geq 0 \mapsto \xm{M}{a}$) 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 $p \in M$. 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 $M$).
Fichier principal
Vignette du fichier
mass_topological.pdf (223.79 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01818684 , version 1 (19-06-2018)

Identifiers

Cite

Andreas Hermann, Emmanuel Humbert. Mass functions of a compact manifold. 2018. ⟨hal-01818684⟩
144 View
74 Download

Altmetric

Share

Gmail Facebook X LinkedIn More