Bishop and Laplacian Comparison Theorems on Three Dimensional Contact Subriemannian Manifolds with Symmetry
Andrei Agrachev, Paul W.Y. Lee
TL;DR
This paper establishes Bishop volume and Laplacian comparison theorems for three-dimensional contact subriemannian manifolds with symmetry, extending geometric analysis tools to this specialized setting.
Contribution
It introduces new comparison theorems specifically tailored for symmetric three-dimensional contact subriemannian manifolds, advancing geometric understanding in this area.
Findings
Proved Bishop volume comparison theorem for the setting.
Established Laplacian comparison theorem under symmetry conditions.
Extended classical comparison theorems to subriemannian contact manifolds.
Abstract
We prove a Bishop volume comparison theorem and a Laplacian comparison theorem for three dimensional contact subriemannian manifolds with symmetry.
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Taxonomy
TopicsGeometric Analysis and Curvature Flows · Point processes and geometric inequalities · Geometric and Algebraic Topology