Première valeur propre du laplacien, volume conforme et chirurgies

Original · EN

We define a new differential invariant a compact manifold by Vₘ(M)= Vc(M,[g]), where Vc(M,[g]) is the conformal volume of M for the conformal class [g], and prove that it is uniformly bounded above. The main motivation is that this bound provides a upper bound of the Friedlander-Nadirashvili invariant defined by g∈[g]λ₁(M, g)(M, g) 2n. The proof relies on the study of the behaviour of Vₘ(M) when one performs surgeries on M.