Convergence of semi-convex functions in CAT(1)-spaces

Gál, Hedvig and Pálfia, Miklós (2024) Convergence of semi-convex functions in CAT(1)-spaces. Calculus of Variations and Partial Differential Equations, 63 (8). DOI 10.1007/s00526-024-02823-4

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Official URL: https://doi.org/10.1007/s00526-024-02823-4

Abstract

We generalize the results of Kuwae–Shioya and Bačák on Mosco convergence established for CAT(0)-spaces to the CAT(1)-setting, so that Mosco convergence implies convergence of resolvents which in turn imply convergence of gradient flows for lower-semicontinuous semi-convex functions. Our techniques utilize weak convergence in CAT(1)-spaces and also cover asymptotic relations of sequences of such spaces introduced by Kuwae-Shioya, including Gromov–Hausdorff limits.

Item Type:

Article

Uncontrolled Keywords:

semi-convex functions ; CAT(1)-spaces

Divisions:

Institute of Data Analytics and Information Systems
Corvinus Doctoral Schools

Subjects:

Mathematics, Econometrics

DOI:

10.1007/s00526-024-02823-4

ID Code:

10326