Volume renormalization for the Blaschke metric on strictly convex domains

Taiji Marugame

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arXiv · 1601.06948

Volume renormalization for the Blaschke metric on strictly convex domains

Taiji Marugame

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Abstract

We consider the volume expansion of the Blaschke metric, which is a projectively invariant metric on a strictly convex domain in a locally flat projective manifold. When the boundary is even dimensional, we express the logarithmic coefficient L as the integral of affine invariants over the boundary. We also formulate an intrinsic geometry of the boundary as a conformal Codazzi structure and show that L gives a global conformal invariant of the boundary.

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Taiji Marugame. 2016-01-26. Volume renormalization for the Blaschke metric on strictly convex domains. https://arxiv.org/abs/1601.06948

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