Local convexity of renormalized volume for rank-1 cusped manifolds

2015/05/03 by Pallete, Franco Vargas
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1505.00479

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.

Related

• Renormalized volume on the Teichmüller space of punctured surfaces
• Convexity of the renormalized volume of hyperbolic 3-manifolds
• Continuity of the renormalized volume under geometric limits
• Renormalized volume and the volume of the convex core
• The renormalized volume and the volume of the convex core of quasifuchsian manifolds