Communications in Analysis and Geometry

Volume 26 (2018)

Number 1

Uniqueness of Schrödinger flow on manifolds

Pages: 217 – 235

DOI: https://dx.doi.org/10.4310/CAG.2018.v26.n1.a5

Authors

Chong Song (School of Mathematical Sciences, Xiamen University, Xiamen, China)

Youde Wang (School of Mathematics & Information Science, Guangzhou University, Guangzhou, China; Academy of Mathematics & Systematic Sciences, CAS, Beijing, China; and School of Mathematical Sciences, University of CAS, Beijing, China)

Abstract

In this paper, we show the uniqueness of Schrödinger flow from a general complete Riemannian manifold to a complete Kähler manifold with bounded geometry. While following the ideas of McGahagan [An approximation scheme for Schrödinger maps, Comm. Partial Differential Equations 32 (2007), no. 1-3, 375–400], we present a more intrinsic proof by using the distance functions and gauge language.

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The first author is supported by Natural Science Foundation of Fujian Province of China (No. 2014J01023) and Fundamental Research Funds for the Central University (No. 20720170009). The second author is supported by NSFC (No. 11471316).

Received 4 August 2016

Published 31 January 2018