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Hilbert-Perelman's functional and Lagrange multipliers


Author: Santiago R. Simanca
Journal: Proc. Amer. Math. Soc. 140 (2012), 4309-4318
MSC (2010): Primary 53C55, 58E11; Secondary 53C21
DOI: https://doi.org/10.1090/S0002-9939-2012-11414-5
Published electronically: July 3, 2012
MathSciNet review: 2957221
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Abstract: We use the Hilbert-Perelman functional over a suitable subspace of its domain and rederive the extremal Kähler flow equation by using the ensuing Lagrange multipliers. We modify the said functional appropriately to present this pseudo-differential equation as a gradient flow and, as a consequence, to show that some of Perelman's monotonicity results hold in this context also.


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Additional Information

Santiago R. Simanca
Affiliation: Laboratoire de Mathématiques Jean Leray, 2, rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
Email: srsimanca@gmail.com

DOI: https://doi.org/10.1090/S0002-9939-2012-11414-5
Received by editor(s): September 20, 2010
Published electronically: July 3, 2012
Communicated by: Varghese Mathai
Article copyright: © Copyright 2012 American Mathematical Society

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