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The generalization of Hartogs' Theorem
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I know a version of Hartogs' Theorem in the book An introduction to complex analysis(p 30) by Hormander, namely
Hartogs' Theorem when K compact with complement being simply connected
I also have learned another version in Hodge Theory and Complex Algebraic Geometry I (p34) by Voisin. Hartogs' Theorem when $K=z_1=z_2=0$
My question: are there any generalizations of Hartogs' Theorem, with respect to $K$ (i.e. we only change the condition of $K$, confining the stage in $mathbbC^n$ )?
Any clue is welcome. Many Thanks!
complex-analysis
asked Jul 27 at 4:48
Littlewood
61
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up vote
1
down vote
favorite
I know a version of Hartogs' Theorem in the book An introduction to complex analysis(p 30) by Hormander, namely
Hartogs' Theorem when K compact with complement being simply connected
I also have learned another version in Hodge Theory and Complex Algebraic Geometry I (p34) by Voisin. Hartogs' Theorem when $K=z_1=z_2=0$
My question: are there any generalizations of Hartogs' Theorem, with respect to $K$ (i.e. we only change the condition of $K$, confining the stage in $mathbbC^n$ )?
Any clue is welcome. Many Thanks!
complex-analysis
asked Jul 27 at 4:48
Littlewood
61
add a comment |Â
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I know a version of Hartogs' Theorem in the book An introduction to complex analysis(p 30) by Hormander, namely
Hartogs' Theorem when K compact with complement being simply connected
I also have learned another version in Hodge Theory and Complex Algebraic Geometry I (p34) by Voisin. Hartogs' Theorem when $K=z_1=z_2=0$
My question: are there any generalizations of Hartogs' Theorem, with respect to $K$ (i.e. we only change the condition of $K$, confining the stage in $mathbbC^n$ )?
Any clue is welcome. Many Thanks!
complex-analysis
asked Jul 27 at 4:48
Littlewood
61
I know a version of Hartogs' Theorem in the book An introduction to complex analysis(p 30) by Hormander, namely
Hartogs' Theorem when K compact with complement being simply connected
I also have learned another version in Hodge Theory and Complex Algebraic Geometry I (p34) by Voisin. Hartogs' Theorem when $K=z_1=z_2=0$
My question: are there any generalizations of Hartogs' Theorem, with respect to $K$ (i.e. we only change the condition of $K$, confining the stage in $mathbbC^n$ )?
Any clue is welcome. Many Thanks!
complex-analysis
asked Jul 27 at 4:48
Littlewood
61
asked Jul 27 at 4:48
Littlewood
61
asked Jul 27 at 4:48
Littlewood
61
asked Jul 27 at 4:48
Littlewood
61
61
add a comment |Â
add a comment |Â
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