欧氏空间中超曲面的一个共形不变式的极值问题

EXTREMAL PROBLEMS OF A CONFORMAL INVARIANT OF HYPERSURFACES IN EUCLIDEAN SPACE

本文研究欧氏空间E^(n+1)中,半径比为1:n^(1/2)的标准超环面,是否在环面浸入范围内,使一个共形不变的积分式达到极小位的问题,对于2≤n≤11的情形,证明半径比1:n^(1/2)的标准超环面的共形积分不变式的值,在标准超环面范围内取到最小值.

In this paper,the author studies following problem:whether do standard hypertorus in E^(n-1) whose radius ratio is 1:n^(1/2) make a conformal integral invariant obtain minimal value?In the case of 2≤n≤11,he proves that conformalintegral invariant of the standard hypertorus with radius ratio 1:n^(1/2) obtains minimal volue in the range of the standardhypertorus.