论文标题
较弱的唯一性，用于节能的平均曲率流量
Weak-strong uniqueness for volume-preserving mean curvature flow
论文作者
论文摘要
在本说明中，我们得出了稳定性的稳定性和虚弱的唯一原理，用于保存体积的平均曲率流。该证明是基于一个新的节能梯度流量校准的新概念，这是Fischer等人最近引入的情况下的概念的自然扩展。 [Arxiv：2003.05478]。第一个主要结果表明，具有某些规律性的任何强溶液都已校准。第二个主要结果由相对熵的稳定性估计值组成，该相对熵在分布解决方案的类别中有效，用于量化体积的平均曲率流。
In this note, we derive a stability and weak-strong uniqueness principle for volume-preserving mean curvature flow. The proof is based on a new notion of volume-preserving gradient flow calibrations, which is a natural extension of the concept in the case without volume preservation recently introduced by Fischer et al. [arXiv:2003.05478]. The first main result shows that any strong solution with certain regularity is calibrated. The second main result consists of a stability estimate in terms of a relative entropy, which is valid in the class of distributional solutions to volume-preserving mean curvature flow.
