标题： 非最小化$p$-调和映射在孤立奇点处的非唯一切映射 显示英文标题

标题： Nonunique tangent maps at isolated singularities of minimizing $p$-harmonic maps

摘要： 在能量极小映射的奇异点处对“切映射”的分析在其对奇异集精细结构的理解中起着重要作用。 此注释给出了一个在孤立奇点处具有非唯一切映射的极小（不仅仅是稳定）$p$-调和映射的第一个例子。 我们构造了一个$n$维流形$N$，使得对于每个可接受的元组$p< m\le n+2$，存在一个从$B_1^m$到$N$的映射，该映射最小化$p$-能量，在原点处有一个孤立奇点，并且具有连续的不同切映射。 该构造建立并扩展了B. White在平稳情况下的$p=2$例子。 显示英文摘要

摘要： The analysis of ``tangent maps'' at singular points of energy minimizing maps plays an important role in our understanding of the fine structure of the singular set. This note presents the first example of a minimizing (not just stationary) $p$-harmonic map with nonunique tangent maps at an isolated singularity. We construct a $n$-dimensional manifold $N$ such that for every admissible tuple $p< m\le n+2$, there exists a map from $B_1^m$ into $N$ that minimizes the $p$-energy, has an isolated singularity at the origin and admits a continuum of distinct tangent maps. The construction builds upon and extends B.~ White's example for $p=2$ in the stationary case.