Precise estimates for certain distances in ℝ^d

2024/12/13 by Fiacchi, Matteo, Nikolov, Nikolai
#32F45 #53A10 #53C23 #Complex Variables (math.CV) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.2412.10012

Abstract

We provide sharp estimates for the intrinsic distances of Finsler metrics with precise boundary estimates. These metrics include the Kobayashi-Hilbert metric near strongly convex points, the minimal metric near convex and strongly minimally convex points, and the k-quasi hyperbolic metric in k-strongly convex domains. Finally, we prove a characterization result in convex geometry for the k-quasi hyperbolic metric.

Related

• Regularity of the distance function to the boundary
• Intrinsic metrics defined with arithmetic and logarithmic mean values
• Estimates of the Kobayashi metric and Gromov hyperbolicity on convex domains of finite type
• The Thurston metric on hyperbolic domains and boundaries of convex hulls
• Complete complex Finsler metrics and uniform equivalence of the Kobayashi metric