A volume comparison theorem for characteristic numbers

Abstract: We show that assuming lower bounds on the Ricci curvature and the injectivity radius the absolute value of any characteristic number of a Riemannian manifold M is bounded proportional to the volume, i.e. bounded by Cvol(M) where C depends only on the characteristic number, the dimension of M, and both bounds. The proof relies on the definition of a connection for an harmonic Hölder regular metric tensor as they appear for instance as Gromov-Hausdorff limits of Riemannian manifolds.

Mathematics

Audience: researchers in the topic

mms&convergence

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Meeting ID: 845 0642 1108 Passcode: 182795