报告人：李本伶（宁波大学）

报告时间：2026年4月17日10：30- 11：30

报告地点：腾讯会议218-603-816

题目：Hilbert's fourth problem in the constant curvature setting

摘要：Hilbert's fourth problem asks for the characterization of metric geometries in which straight line segments are shortest paths. In this talk, I will discuss recent progress on this problem within the framework of projectively flat Finsler metrics with constant flag curvature—a setting where the global structure has long remained a subtle and challenging topic.

Instead of presenting only final results, I will focus on the ideas and developments that have led to a better global understanding. In particular, I will explain how explicit distance formulas emerge, describe the classification achieved in the non-positive curvature case, and discuss why, in the positive curvature case, the metric completion must be a sphere. I will also highlight an unexpected link to the nonlinearity of Sobolev spaces, and present several new examples of exotic metrics defined on evolving domains.

These findings contribute to a more unified picture of the global geometry in this classical setting. This is joint work with Wei Zhao.

报告人简介：李本伶，浙江宁波人，2007年毕业于浙江大学数学系，获理学博士学位。现任宁波大学数学与统计学院教授，宁波市数学学会副理事长。研究领域为微分几何，主要从事Finsler几何和Spray几何的研究，在Adv. Math, Comm. Anal. Geom., Sci. China Math., Differential Geom. Appl.等期刊上发表多篇论文。主持完成国家自然科学基金项目、浙江省自然科学基金杰出青年项目等多项课题。