Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces

Chao Li

Research output: Contribution to journalArticlepeer-review


In this note, we establish the dihedral rigidity phenomenon for a collection of parabolic polyhedrons enclosed by horospheres in hyperbolic manifolds, extending Gro-mov’s comparison theory to metrics with negative scalar curvature lower bounds. Our result is a localization of the positive mass theorem for asymptotically hyperbolic manifolds. We also motivate and formulate some open questions concerning related rigidity phenomenon and convergence of metrics with scalar curvature lower bounds.

Original languageEnglish (US)
Article number099
JournalSymmetry, Integrability and Geometry: Methods and Applications (SIGMA)
StatePublished - 2020


  • Comparison theorem
  • Dihedral rigidity
  • Hyperbolic manifolds
  • Scalar curvature

ASJC Scopus subject areas

  • Analysis
  • Mathematical Physics
  • Geometry and Topology


Dive into the research topics of 'Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces'. Together they form a unique fingerprint.

Cite this