We construct a rectifiable stationary 2-varifold in R^4 with non-conical, andhence non-unique, tangent varifold at a point. This answers a question of L.Simon (Lectures on geometric measure theory, 1983, p. 243) and provides a newexample for a related question of W.K. Allard (On the first variation of avarifold, Ann. of Math., 1972, p. 460). There is also a (rectifiable) stationary 2-varifold in R^4 that has more thanone conical tangent varifold at a point. keywords: stationary varifold, varifold tangent, tangent cone, non-unique,non-conical, minimal surface, regularity
展开▼
机译:我们在R ^ 4中构造了一个可校正的平稳2变量,该变量在一点处具有非圆锥形,因此具有非唯一切线变量。这回答了西蒙(L.Simon)的一个问题(几何测量理论讲座,1983年,第243页),并为W.K.阿拉德(关于avarifold的第一个变化,《数学年鉴》,1972年,第460页)。 R ^ 4中还有一个(可校正的)平稳2变量,该变量在一个点上有多个圆锥形切线变量。关键字:固定变量,变量正切,圆锥锥,非唯一,非圆锥,最小表面,规则性
展开▼