中科院数学与系统科学研究院
数学研究所
几何分析研讨班
报告人：SUN Ao (University of Chicago)
题 目：Uniqueness problem in mean curvature flow
时 间：2021.03.23（星期二）, 09:00-1100 2021.03.30（星期二）, 09:00-11:00
地 点：腾讯会议ID 518 7997 8794
摘 要：In this sequel of talks, we will discuss an important geometric heat flow called mean curvature flow, and we will mainly focus on the uniqueness problem in mean curvature flow. The initial arrangement of the talks is as follows:
First, I will discuss some basic properties of mean curvature flow. In particular, we will discuss the models of singularities, especially the model of the tangent flow called self-shrinkers.
Next, I will introduce the Lojasiewicz inequality, which is a fundamental inequality in real algebraic geometry. In a pioneer work, Leon Simon discovered that Lojasiewicz inequality is very useful in the study of variational problems. I will discuss the applications of Lojasiewicz inequality in mean curvature flow, especially how to use it to prove the tangent flows are unique.
Finally, I will discuss an alternative approach to Lojasiewicz inequality, which allows us to obtain a quantitative Lojasiewicz inequality near some special self-shrinkers of mean curvature flow. In particular, I will discuss joint work with Jonathan Zhu on the local uniqueness of Clifford self-shrinkers in higher codimensions.
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报告人：SUN Ao (University of Chicago)
题 目：Uniqueness problem in mean curvature flow
时 间：2021.03.26（星期五）, 09:00-11:00 2021.04.02（星期五）, 09:00-11:00
地 点：腾讯会议523 8743 9604
摘 要：In this sequel of talks, we will discuss an important geometric heat flow called mean curvature flow, and we will mainly focus on the uniqueness problem in mean curvature flow. The initial arrangement of the talks is as follows:
First, I will discuss some basic properties of mean curvature flow. In particular, we will discuss the models of singularities, especially the model of the tangent flow called self-shrinkers.
Next, I will introduce the Lojasiewicz inequality, which is a fundamental inequality in real algebraic geometry. In a pioneer work, Leon Simon discovered that Lojasiewicz inequality is very useful in the study of variational problems. I will discuss the applications of Lojasiewicz inequality in mean curvature flow, especially how to use it to prove the tangent flows are unique.
Finally, I will discuss an alternative approach to Lojasiewicz inequality, which allows us to obtain a quantitative Lojasiewicz inequality near some special self-shrinkers of mean curvature flow. In particular, I will discuss joint work with Jonathan Zhu on the local uniqueness of Clifford self-shrinkers in higher codimensions.
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