McShane-type Identities for Affine Deformations
Virginie Charette, William M. Goldman
TL;DR
This paper extends McShane-type identities to affine deformations of hyperbolic surfaces, showing that infinitesimal lengthening of interior curves implies boundary lengthening, with implications for understanding surface deformations.
Contribution
It derives a new identity for Margulis invariants in affine deformations, generalizing classical identities to a broader geometric context.
Findings
Infinitesimal lengthening of interior curves implies boundary lengthening.
Derived a new identity for Margulis invariants in affine deformations.
Extended classical identities to affine deformation settings.
Abstract
We derive an identity for Margulis invariants of affine deformations of a complete orientable one-ended hyperbolic sur- face following the identities of McShane, Mirzakhani and Tan- Wong-Zhang. As a corollary, a deformation of the surface which infinitesimally lengthens all interior simple closed curves must in- finitesimally lengthen the boundary.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometric and Algebraic Topology · Geometric Analysis and Curvature Flows · Homotopy and Cohomology in Algebraic Topology