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arXiv · 1505.00479

Local convexity of renormalized volume for rank-1 cusped manifolds

Franco Vargas Pallete
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Abstract

We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a modified definition of the renormalized volume that is additive under gluing, and study some local properties.

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Franco Vargas Pallete. 2015-05-03. Local convexity of renormalized volume for rank-1 cusped manifolds. https://arxiv.org/abs/1505.00479

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