广州数学大讲坛第二期

第十一讲——英国巴斯大学Manuel del Pino教授学术报告

题目：Compact Equilibria in the Liquid Drop Model

时间：2026年1月18 日（周日）16:30-18:00

地点：行政西前座334会议室

报告人：Manuel del Pino 教授

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.

报告人简介：

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. Manuel 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。 Manuel 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 Math. J. 等国际顶级期刊。 Manuel 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院士，the Chilean National Award in 2013，the recipient of a Research Professorship from the UK Royal Society (2018-2023).