Hilbert-Perelman’s functional and Lagrange multipliers
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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.References
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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
- Received by editor(s): September 20, 2010
- Published electronically: July 3, 2012
- Communicated by: Varghese Mathai
- © Copyright 2012 American Mathematical Society
- 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
- MathSciNet review: 2957221