Conformal Transformation on Metric Measure Spaces

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Abstract

We study several problems concerning conformal transformation on metric measure spaces, including the Sobolev space, the differential structure and the curvature-dimension condition under conformal transformations. This is the first result about preservation of lower curvature bounds under perturbation, which is new even on Alexandrov spaces.

Keywords

Curvature-dimension condition Bakry-Émery theory Conformal transformation Ricci tensor Metric measure space 

Mathematics Subject Classification (2010)

31E05 53C23 51F99 30L99 

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Notes

Acknowledgements

The author acknowledges the support of the HCM fellowship, and he thanks Prof. Karl-Theodor Sturm for proposing this topic and valuable advice. The author also wants to thank the reviewer for helpful remarks and suggestions.

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© Springer Science+Business Media B.V., part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute for Applied MathematicsUniversity of BonnBonnGermany

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