Effective equidistribution of intersection points in hyperbolic manifolds

2025/11/30 by Tina Torkaman, Torkaman, Tina, Yongquan Zhang +1
Mathematics · #Mathematical Dynamics and Fractals #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2512.01143

Abstract

In this paper, we establish effective equidistribution of transverse intersection points between properly immersed totally geodesic submanifolds of complementary dimensions in a finite-volume hyperbolic manifold with respect to the hyperbolic volume measure, as the volume of the submanifolds tends to infinity.

Citations

• Finiteness of totally geodesic hypersurfaces
• Intersection Points of Closed Geodesics on Hyperbolic Surfaces of Finite Area
• Effective equidistribution of orbits under semisimple groups on congruence quotients
• Arithmeticity, Superrigidity, and Totally Geodesic Submanifolds
• Arithmeticity of hyperbolic 3-manifolds containing infinitely many\n totally geodesic surfaces
• Equidistribution of minimal hypersurfaces for generic metrics
• Closed geodesics and holonomies for Kleinian manifolds
• Self-intersections in combinatorial topology: statistical structure
• Self-Intersections of Random Geodesics on Negatively Curved Surfaces
• Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces

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