Complex manifolds of Sobolev mappings and a Hartogs-type theorem in loop spaces

ABSTRACT

We recall the complex structure on the generalized loop spaces $W^{k,2}(S,X)$, where S is a compact real manifold with boundary and X is a complex manifold, and prove a Hartogs-type extension theorem for holomorphic maps from certain domains in generalized loop spaces.

KEYWORDS:

• Hilbert-Hartogs manifold
• analytic continuation
• Sobolev spaces

AMS SUBJECT CLASSIFICATION:

• Several complex variables

Acknowledgements

I would like to express my gratitude and thanks to my PhD advisor for encouraging me to keep going on research in mathematics. I am also grateful to my wife and my parents for their continuous support to me throughout this work.

Disclosure statement

No potential conflict of interest was reported by the author.