TY - JOUR
T1 - Graham-Witten's Conformal Invariant for Closed Four Dimensional Submanifolds
AU - Zhang , Yongbing
JO - Journal of Mathematical Study
VL - 2
SP - 200
EP - 226
PY - 2021
DA - 2021/02
SN - 54
DO - http://doi.org/10.4208/jms.v54n2.21.06
UR - https://global-sci.org/intro/article_detail/jms/18617.html
KW - Minimal surface, AdS/CFT, conformal invariant.
AB - <p>It was proved by Graham and Witten in 1999 that conformal invariants of submanifolds can be obtained via volume renormalization of&nbsp; 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&#39;s conformal invariant for closed four dimensional submanifolds and find critical points of the conformal invariant in the case of Euclidean ambient spaces.</p>