Local convexity of renormalized volume for rank-1 cusped manifolds
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.
