Graham-Witten's Conformal Invariant for Closed Four Dimensional Submanifolds

DOI10.4208/JMS.V54N2.21.06zbMATH Open1474.53194arXiv1703.08611OpenAlexW3128634812MaRDI QIDQ4996008

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Publication date: 1 July 2021

Published in: (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/1703.08611

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