带边界曲面上正曲率 ancient Ricci 流的唯一性
Uniqueness of positively curved ancient Ricci flows on surfaces with boundary
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中文总结 AI 辅助
本文证明了满足直径一致有界、边界测地曲率为正常数的二维带边界曲面上正曲率 ancient Ricci 流的存在与唯一性，该流具旋转对称性，其极限行为明确，是带边界 ancient Ricci 流分类的首个结果。
中文摘要 AI 辅助
在假设直径一致有界且边界测地曲率为正常数的条件下，我们建立了二维带边界曲面（M², ∂M², g(t)）上正曲率 ancient Ricci 流在不依赖时间的微分同胚下的存在性与唯一性。特别地，该 ancient Ricci 流具有旋转对称性，其向后极限为平坦圆盘，向前极限为半球形奇点。据我们所知，该结果是带边界 ancient Ricci 流分类结果的首个实例。
英文摘要
We establish the existence and uniqueness modulo time-independent diffeomorphisms of the positively curved ancient Ricci flow $(M^2, \partial M^2, g(t))$ on a two-dimensional surface with boundary, assuming uniformly bounded diameter and constant positive boundary geodesic curvature. In particular, this ancient Ricci flow is rotationally symmetric, its backward limit is the flat disk, and its forward limit is a half-spherical singularity. To our knowledge, this result is the first instance of a classification result for ancient Ricci flows with boundary.
