Identification of a Connection from Cauchy Data on a Riemann Surface with Boundary

被引：24

作者：

Guillarmou, Colin ^{[1
]}

Tzou, Leo ^{[2
,3
]}

机构：

[1] Ecole Normale Super, CNRS, DMA, UMR 8553, F-75230 Paris, France

[2] Stanford Univ, Dept Math, Stanford, CA 94305 USA

[3] Univ Helsinki, Dept Math, Helsinki 00014, Finland

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2011年 / 21卷 / 02期

关键词：

Calderon inverse problems; Cauchy data space; magnetic Schrodinger operator; Riemann surfaces; connection Laplacian; 2; DIMENSIONS; SCHRODINGER-EQUATION; VECTOR POTENTIALS; INVERSE; OPERATOR;

D O I：

10.1007/s00039-011-0110-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a connection del(x) on a complex line bundle over a Riemann surface with boundary M (0), with connection 1-form X. We show that the Cauchy data space of the connection Laplacian (also called magnetic Laplacian) L:=del(x*)del(x) + q, with q a complex-valued potential, uniquely determines the connection up to gauge isomorphism, and the potential q.

引用

页码：393 / 418

页数：26

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