On Perelman's Dilaton
Differential Geometry
2010-05-31 v1 Analysis of PDEs
Abstract
By means of a Kaluza-Klein type argument we show that the Perelman's F-functional is the Einstein-Hilbert action in a space with extra ``phantom'' dimensions. In this way, we try to interpret some remarks of Perelman in the introduction and at the end of the first section in his first famous paper. As a consequence the Ricci flow (modified by a diffeomorphism and a time-dependent factor) is the evolution of the ``real'' part of the metric under a constrained gradient flow of the Einstein-Hilbert gravitational action in higher dimension.
Cite
@article{arxiv.0805.3268,
title = {On Perelman's Dilaton},
author = {Marco Caldarelli and Giovanni Catino and Zindine Djadli and Annibale Magni and Carlo Mantegazza},
journal= {arXiv preprint arXiv:0805.3268},
year = {2010}
}