Hilbert's fourth problem: the constant curvature case

报告人：李本伶（宁波大学）

时  间：2026年6月9日10:00

地  点：海韵园实验楼S204

内容摘要:

Hilbert's fourth problem asks for the characterization of metric geometries in which straight line segments are shortest paths. Its regular case is to classify projectively flat Finsler metrics. In this talk, we discuss recent progress on this problem within the framework of constant curvature — a setting where the global structure has long remained a subtle and challenging topic. Instead of presenting only final results, the focus is on the ideas and developments that have led to a better global understanding. We 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. An unexpected link to the nonlinearity of Sobolev spaces is also highlighted, together with several new examples of exotic metrics defined on evolving domains.

个人简介：

李本伶，宁波大学数学与统计学院教授，宁波市数学学会副理事长。2007年毕业于浙江大学数学系，获理学博士学位。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课题。

联系人：桂耀挺