Improvements of upper curvature bounds
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- by Alexander Lytchak and Stephan Stadler PDF
- Trans. Amer. Math. Soc. 373 (2020), 7153-7166 Request permission
Abstract:
We prove that upper curvature bounds in the sense of Alexandrov can be improved locally by using appropriate conformal changes. As a new technical tool we derive a generalization to metric spaces and semi-convex functions of the classical differential geometric property that compositions of harmonic maps with convex functions are subharmonic.References
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Additional Information
- Alexander Lytchak
- Affiliation: Mathematisches Institut, Universität Köln, Weyertal 86–90, 50931, Köln, Germany
- MR Author ID: 679338
- Email: alytchak@math.uni-koeln.de
- Stephan Stadler
- Affiliation: Mathematisches Institut der Universität München, Theresienstrasse 39, D-80333 München, Germany
- MR Author ID: 1136806
- Email: stadler@math.lmu.de
- Received by editor(s): November 8, 2019
- Received by editor(s) in revised form: January 20, 2020
- Published electronically: August 5, 2020
- Additional Notes: Both authors were partially supported by DFG grant SPP 2026.
- © Copyright 2020 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 373 (2020), 7153-7166
- MSC (2010): Primary 53C20, 53C23, 58E20
- DOI: https://doi.org/10.1090/tran/8123
- MathSciNet review: 4155203