The simplex lemma of Logunov(洛古诺夫的单纯形引理)

摘要：In this talk, we will give an analytic proof of the simplex lemma of Alexander Logunov, which appeared in his famous paper published in the Annals of Mathematics in 2018 as a cornerstone of the polynomial upper estimates of the Hausdorff measure of the nodal sets of Laplace eigenfunctions, stated, without giving a proof, that one can always cover a Euclidean simplex using large balls centered at its vertexes, such that the union of the balls contains a larger ball centered at the mass center of the simplex, with universal ratios of the radiuses, depending only on the diameter and width of the simplex.

李志夙，西北大学数学学院、非线性科学研究中心副教授，博士研究生导师。博士毕业于西安交通大学；曾在北京大学北京国际数学研究中心任助理研究员和博士后。主要研究方向为偏微分方程和微分几何。近期已有的研究成果主要涉及奇异完全非线性椭圆方程的 $W^{2,\delta}$ 正则性，海森商方程和特殊拉格朗日方程的外狄利克雷问题，以及一大类几何完全非线性退化椭圆方程的外刚性问题等；均分别以学术论文形式先后在 Mathematische Zeitschrift，Journal of Differential Equations，Transactions of the American Mathematical Society 和 Advances in Mathematics 等国际著名期刊上发表。主持国家自然科学基金面上项目；且获得陕西省青年人才项目支持。