Year: 2021
Author: Yongbing Zhang
Journal of Mathematical Study, Vol. 54 (2021), Iss. 2 : pp. 200–226
Abstract
It was proved by Graham and Witten in 1999 that conformal invariants of submanifolds can be obtained via volume renormalization of minimal surfaces in conformally compact Einstein manifolds. The conformal invariant of a submanifold $\Sigma$ is contained in the volume expansion of the minimal surface which is asymptotic to $\Sigma$ when the minimal surface approaches the conformaly infinity. In the paper we give the explicit expression of Graham-Witten's conformal invariant for closed four dimensional submanifolds and find critical points of the conformal invariant in the case of Euclidean ambient spaces.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jms.v54n2.21.06
Journal of Mathematical Study, Vol. 54 (2021), Iss. 2 : pp. 200–226
Published online: 2021-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 27
Keywords: Minimal surface AdS/CFT conformal invariant.