学术报告报告主题: Compact Equilibria in the Liquid Drop Model
报 告 人: Manuel del Pino教授（University of Bath）
报告时间： 2026年1月17 日（星期六）下午4:10-5:10
报告地点： 37号楼 3A02
邀 请 人: 程永宽副教授
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数学学院
2026年1月13日
报告摘要：
This work addresses the liquid drop model, introduced by Gamow in 1930 and Bohr–Wheeler in 1939, to describe the structure of atomic nuclei in nuclear physics. The problem involves finding a surface in three-dimensional space that is critical for a specific energy functional, balancing surface tension and nonlocal repulsion, subject to a volume constraint. Spherical solutions always exist and minimize the energy for sufficiently small volumes. However, for larger volumes, constructing non-minimizing critical points becomes more challenging. In this study, we present a new class of large-volume solutions, resembling “pearl collars” arranged along an axis in the shape of a large circle, with geometry close to Delaunay’s unduloids—surfaces of constant mean curvature. We also construct non-minimizing solutions with small mass that resemble two nearly identical spheres connected by a narrow neck.
This is collaboration with Mónica Musso, Andrés Zúñiga, and Rupert Frank.
报告人介绍：
Manuel del Pino, 英国University of Bath数学系教授，国际知名数学家，主要从事Analysis of nonlinear partial differential equations, Blow-up patterns in nonlinear evolution problems, Singular limits in variational problems with loss of compactness.del Pino与合作者在 asymptotic patterns insingular perturbation problems and singularity formation in time dependent settings做出一系列开创新的结果，开辟了parabolic gluing 方法。del Pino已经发表了超过170余篇论文，其中包括了著名的De Giorgi猜想的反例, 开创新地引进parabolic gluing方法在临界热方程， 平面harmonic map flow奇性解的构造，在Mathscinet上引用已达7000多次。Manuel的学术成果发表在Ann. of Math.， Invent. Math.,J. Eur. Math. Soc., CPAM, Duke 等国际顶级期刊。del Pino获得过很多荣誉，其中包括2010 ICM 45分钟报告，2013成为Chilean Academy of Sciences会员，the Chilean National Award in 2013，the recipient of a Research Professorship from the UK Royal Society (2018-2023).