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The Linearized Calderón Problem on Complex Manifolds
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作者 colin guillarmou Mikko SALO Leo TZOU 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2019年第6期1043-1056,共14页
In this note we show that on any compact subdomain of a K?hler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer ... In this note we show that on any compact subdomain of a K?hler manifold that admits sufficiently many global holomorphic functions, the products of harmonic functions form a complete set. This gives a positive answer to the linearized anisotropic Calderón problem on a class of complex manifolds that includes compact subdomains of Stein manifolds and sufficiently small subdomains of K?hler manifolds. Some of these manifolds do not admit limiting Carleman weights, and thus cannot be treated by standard methods for the Calderón problem in higher dimensions. The argument is based on constructing Morse holomorphic functions with approximately prescribed critical points. This extends earlier results from the case of Riemann surfaces to higher dimensional complex manifolds. 展开更多
关键词 INVERSE PROBLEM Calderón PROBLEM COMPLEX MANIFOLD
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