Optimal bounds for the Kobayashi distance near \mathcal C²-smooth boundary points

2025/06/06 by Николай Николов, Nikolov, Nikolai, Pascal J. Thomas +1
Mathematics · #Holomorphic and Operator Theory #Advanced Harmonic Analysis Research #Geometric Analysis and Curvature Flows

paper · pdf · doi:10.48550/arxiv.2506.06507

Abstract

It is shown that the optimal upper and lower bounds for the Kobayashi distance near \mathcal C^2,α-smooth strongly pseudoconvex boundary points obtained in L. Kosinski, N. Nikolov, A.Y. Okten: "Precise estimates of invariant distances on strongly pseudoconvex domains", Adv. Math. 478 (2025), 110388, remain true in the general \mathcal C² strongly pseudoconvex setting. In fact, the upper bound is extended to the general \mathcal C^1,1-smooth case. We also give upper and lower bounds for the Kobayashi distance near non-semipositive boundary points.

Citations

• Boundary regularity for the distance functions, and the eikonal equation
• Precise estimates of invariant distances on strongly pseudoconvex domains

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