Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

Improvements of upper curvature bounds


Authors: Alexander Lytchak and Stephan Stadler
Journal: Trans. Amer. Math. Soc. 373 (2020), 7153-7166
MSC (2010): Primary 53C20, 53C23, 58E20
DOI: https://doi.org/10.1090/tran/8123
Published electronically: August 5, 2020
MathSciNet review: 4155203
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)

References

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 53C20, 53C23, 58E20

Retrieve articles in all journals with MSC (2010): 53C20, 53C23, 58E20


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

Keywords: Non-positive curvature, conformal change, minimal disc, harmonic maps
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.
Article copyright: © Copyright 2020 American Mathematical Society