基础数学系学术报告

题目: Minimal immersions of conformally flat tori in $S^n$ by the first eigenfunctions

报告人: 谢振肖（中国矿业大学（北京））

时间：2023-04-25 10:00-11:00 (周二上午)

地点: 腾讯会议ID：944-735-382

摘要: Minimal immersions of Riemannian manifolds in $S^n$ by the first eigenfunctions appear naturally in the investigation of conformal volume and related topics in the spectral geometry. As far as we know, the classification of such immersions is known only for 2-sphere and 2-torus. In this talk, we will give a complete classification to conformally flat tori of dimension 3 and 4. Several interesting examples will be discussed, such as a 2-parameter family of non-congruent $\lambda_1$-minimal flat 4-tori. Moreover, for the general dimension n, we prove that there exist only finite many  conformally flat n-tori admitting $\lambda_1$-minimal immersions into spheres.  This is a joint work with Ying Lv and Peng Wang.

报告人简介: 谢振肖，中国矿业大学（北京）副教授，主要从事微分几何方向研究，博士毕业于北京大学，曾访问美国圣路易斯华盛顿大学一年；主要研究成果包括：给出了Wintgen ideal submanifolds的一系列刻画分类定理；在复二次超曲面和复Grassmannian流形G(2,5)中，对常曲率的极小2维球面，构造了一批新的例子，并研究了它们的模空间结构; 给出了3维和4维共形平坦环到球空间中的第一特征极小浸入的完全分类; 在Adv. Math.、Sci. China Math.、Tohoku Math. J.等国际知名期刊发表学术论文十余篇，目前主持国家自然科学基金面上项目一项，完成青年基金一项。

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