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Local convexity of renormalized volume for rank-1 cusped manifolds

Research paper by Franco Vargas Pallete

Indexed on: 03 May '15Published on: 03 May '15Published in: Mathematics - Differential Geometry



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.