标题： 流动映射到极小曲面：解的存在性和唯一性 显示英文标题

标题： Flowing maps to minimal surfaces: Existence and uniqueness of solutions

摘要： 我们研究了在[11]中引入的新几何流，该流以一种方式演化映射和（定义域）度量，使其将适当的初始数据转换为分支极小浸入。 在本文中，我们关注存在性理论以及解的唯一性问题。 我们证明，只要度量保持在模空间的有界区域内，即只要流不将定义域流形中的闭测地线坍塌为一个点，(弱)解就存在。 此外，我们证明在所有非增能量的弱解类中，这个解是唯一的。 这项工作补充了Topping和作者在[11]中的论文，其中介绍了该流，并讨论了其渐近收敛到分支极小浸入的情况。 显示英文摘要

摘要： We study the new geometric flow that was introduced in [11] that evolves a pair of map and (domain) metric in such a way that it changes appropriate initial data into branched minimal immersions. In the present paper we focus on the existence theory as well as the issue of uniqueness of solutions. We establish that a (weak) solution exists for as long as the metrics remain in a bounded region of moduli space, i.e. as long as the flow does not collapse a closed geodesic in the domain manifold to a point. Furthermore, we prove that this solution is unique in the class of all weak solutions with non-increasing energy. This work complements the paper [11] of Topping and the author where the flow was introduced and its asymptotic convergence to branched minimal immersions is discussed.