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Showing 2009 · math.DGShow all
3 papers · 2 filters
math.DG2009★ 2 cited
Relative systoles of relative-essential 2-complexes
Karin U. Katz, Mikhail G. Katz, Stephane Sabourau +2
We prove a systolic inequality for the phi-relative 1-systole of a phi-essential 2-complex, where phi is a homomorphism from the fundamental group of the complex, to a finitely pre…
math.DG2009★ 13 cited
Local extremality of the Calabi-Croke sphere for the length of the shortest closed geodesic
Stephane Sabourau
Recently, F. Balacheff proved that the Calabi-Croke sphere made of two flat 1-unit-side equilateral triangles glued along their boundaries is a local extremum for the length of the…
math.DG2009★ 10 cited
Harmonic spinors and local deformations of the metric
Bernd Ammann, Mattias Dahl, Emmanuel Humbert
Let (M,g) be a compact Riemannian spin manifold. The Atiyah-Singer index theorem yields a lower bound for the dimension of the kernel of the Dirac operator. We prove that this boun…