Real-analytic sub-Riemannian manifolds are constructed with minimizing geodesics that exhibit interior singularities and branching; similar non-smooth branching geodesics exist in Carnot groups via lifting.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Sub-Riemannian manifolds with full-support measures are never CD(K,N) unless Riemannian, and new cone-Grushin RCD spaces on R^n are constructed that are not sub-Riemannian.
A sufficient condition for the quasi Bakry-Émery curvature condition on step-two Carnot groups is established and applied to obtain gradient estimates for the heat semigroup on N_{3,2}.
Rigidity and structure theorems for Busemann spaces with MCP measures under geodesic completeness or non-collapse assumptions.
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On gradient estimates of the heat semigroups on step-two Carnot groups
A sufficient condition for the quasi Bakry-Émery curvature condition on step-two Carnot groups is established and applied to obtain gradient estimates for the heat semigroup on N_{3,2}.