On conformal surfaces of annulus type

[摘要] Let a > b > 0 and B-a \ B-b = { = (x(1), x(2)) is an element of R-2: b < vertical bar x vertical bar < a}, and assume that f is a conformal map from B-a\ B-b into R-n, with vertical bar del f vertical bar(2) = 2e(2)u, then (e(1), e(2)) with e(1) = e(-u) partial derivative f/partial derivative r, and e(2) = r(-1) e(-u) partial derivative f/partial derivative 0 is a moving frame on f(Ba \ Bb) and it satisfies the following equation d(*) < de(1), e(2)> = 0, where (*) is the Hodge star operator on R-2 with respect to the standard metric. We will study the Dirichlet energy of this frame and give some applications. (C) 2012 Elsevier Inc. All rights reserved.

[发布日期] 2012-12-15