Scholarlink

<p>In this paper, we introduce the spherical support function and radial function for spherically convex bodies contained within a hemisphere. Using variational methods for spherical chord integral, we investigate the associated chord measure on the sphere. Our main results establish the weak convergence of this measure and, as a byproduct, demonstrate that the spherical chord measure of a spherically convex body is absolutely continuous with respect to the surface area measure of its gnomonic projection. Furthermore, we propose and solve a Minkowski-type problem associated with the spherical chord measure.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Chord Measure on the Sphere and Associated Minkowski-Type Problem

  • 期刊论文

  • 发表日期：

    2026年3月17日

查看全文
  • Li Sheng,
  • Yin Zhang

摘要

In this paper, we introduce the spherical support function and radial function for spherically convex bodies contained within a hemisphere. Using variational methods for spherical chord integral, we investigate the associated chord measure on the sphere. Our main results establish the weak convergence of this measure and, as a byproduct, demonstrate that the spherical chord measure of a spherically convex body is absolutely continuous with respect to the surface area measure of its gnomonic projection. Furthermore, we propose and solve a Minkowski-type problem associated with the spherical chord measure.