Hilbert-Perelman’s functional and Lagrange multipliers

Simanca, Santiago

doi:10.1090/S0002-9939-2012-11414-5

Hilbert-Perelman’s functional and Lagrange multipliers
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Proc. Amer. Math. Soc. 140 (2012), 4309-4318 Request permission

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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