A Gehring–Hayman Inequality for Strongly Pseudoconvex Domains
Copyright policy )A Gehring–Hayman Inequality for Strongly Pseudoconvex Domains
Abstract We prove that if $D$ is a strongly pseudoconvex domain with $\mathcal C^{2, \alpha }$-smooth boundary, then the length of a geodesic for the Kobayashi–Royden infinitesimal metric between two points is bounded by a constant multiple of the Euclidean distance between the points.
Complex Variables, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], visibility, [MATH] Mathematics [math], Strongly pseudoconvex domains, strongly pseudoconvex domains, Hyperbolic and Kobayashi hyperbolic manifolds, 510, 620, Kobayashi-Royden pseudometric, Kobayashi hyperbolic spaces, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], FOS: Mathematics, [MATH]Mathematics [math], Complex Variables (math.CV), Invariant metrics and pseudodistances in several complex variables, geodesics
Complex Variables, Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV], visibility, [MATH] Mathematics [math], Strongly pseudoconvex domains, strongly pseudoconvex domains, Hyperbolic and Kobayashi hyperbolic manifolds, 510, 620, Kobayashi-Royden pseudometric, Kobayashi hyperbolic spaces, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], FOS: Mathematics, [MATH]Mathematics [math], Complex Variables (math.CV), Invariant metrics and pseudodistances in several complex variables, geodesics
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