Uniqueness of Schr\"odinger flow on manifolds

TL;DR

This paper proves the uniqueness of Schr"odinger flow between complete Riemannian and K"ahler manifolds using an intrinsic approach with distance functions and gauge language.

Contribution

It provides a more intrinsic proof of Schr"odinger flow uniqueness on manifolds, extending previous ideas with new techniques.

Findings

Established the uniqueness of Schr"odinger flow on manifolds.

Developed an intrinsic proof method using distance functions.

Extended the understanding of flow behavior on complex geometric structures.

Abstract

In this paper, we show the uniqueness of Schr\"odinger flow from a general complete Riemannian manifold to a complete K\"ahler manifold with bounded geometry. While following the ideas of McGahagan[16], we present a more intrinsic proof by using the distance functions and gauge language.