Comparison of the Calabi and Mabuchi geometries and applications to geometric flows

Darvas, Tamás

doi:10.1016/j.anihpc.2016.09.002

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Relation To Classical Notions Of Convergence1

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“…The study of this structure was taken up by Calamai [31] and Clarke-Rubinstein [44]. In the latter work the completion of the Calabi path lengh metric was identified, and was compared to the Mabuchi geometry in [49].…”

Section: Relation To Classical Notions Of Convergencementioning

confidence: 99%

Geometric pluripotential theory on Kähler manifolds

Darvas¹

2019

Advances in Complex Geometry

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106

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Finite energy pluripotential theory accommodates the variational theory of equations of complex Monge-Ampère type arising in Kähler geometry. Recently it has been discovered that many of the potential spaces involved have a rich metric geometry, effectively turning the variational problems in question into problems of infinite dimensional convex optimization, yielding existence results for solutions of the underlying complex Monge-Ampère equations. The purpose of this survey is to describe these developments from basic principles. Smith, V. Tosatti and the anonymous referees for their suggested corrections, careful remarks, and precisions. Also, I thank the students of MATH868D at the University of Maryland for their intriguing questions and relentless interest throughout the Fall of 2016. Chapter 3 is partly based on work done as a graduate student at Purdue University, and I am indebted to L. Lempert for encouragement and guidance. Chapter 4 surveys to some extent joint work with Y. Rubinstein, and I am grateful for his mentorship over the years.

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Section: Relation To Classical Notions Of Convergencementioning

confidence: 99%