Local convexity of renormalized volume for rank-1 cusped manifolds

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.

12 pages

References in corpus (3)

• On the renormalized volume of hyperbolic 3-manifolds
• Renormalized volume on the Teichmüller space of punctured surfaces
• Positivity of the renormalized volume of almost-Fuchsian hyperbolic $3$-manifolds

Cited by in corpus (2)

• Renormalized volume on the Teichmüller space of punctured surfaces
• Additive continuity of the renormalized volume under geometric limits