Integration of a (0,1)-form on the boundary of a Riemann surface
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In Simon Donaldson's book, he says that for any (0,1)-form $theta$ on a compact connected Riemann surface $X$, the integral of $partialtheta$ over $X$ is zero by Stokes' theorem - but that seems like he is using that $$int_{partial X}theta=0,$$ and since $X$ might have boundary, how do we know that this is true? Is it even true? He makes a ton of small mistakes, so he might have meant to say a closed Riemann surface.
differential-forms complex-geometry complex-integration riemann-surfaces stokes-theorem
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
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add a comment |
$begingroup$
In Simon Donaldson's book, he says that for any (0,1)-form $theta$ on a compact connected Riemann surface $X$, the integral of $partialtheta$ over $X$ is zero by Stokes' theorem - but that seems like he is using that $$int_{partial X}theta=0,$$ and since $X$ might have boundary, how do we know that this is true? Is it even true? He makes a ton of small mistakes, so he might have meant to say a closed Riemann surface.
differential-forms complex-geometry complex-integration riemann-surfaces stokes-theorem
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
$endgroup$
add a comment |
$begingroup$
In Simon Donaldson's book, he says that for any (0,1)-form $theta$ on a compact connected Riemann surface $X$, the integral of $partialtheta$ over $X$ is zero by Stokes' theorem - but that seems like he is using that $$int_{partial X}theta=0,$$ and since $X$ might have boundary, how do we know that this is true? Is it even true? He makes a ton of small mistakes, so he might have meant to say a closed Riemann surface.
differential-forms complex-geometry complex-integration riemann-surfaces stokes-theorem
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
$endgroup$
In Simon Donaldson's book, he says that for any (0,1)-form $theta$ on a compact connected Riemann surface $X$, the integral of $partialtheta$ over $X$ is zero by Stokes' theorem - but that seems like he is using that $$int_{partial X}theta=0,$$ and since $X$ might have boundary, how do we know that this is true? Is it even true? He makes a ton of small mistakes, so he might have meant to say a closed Riemann surface.
differential-forms complex-geometry complex-integration riemann-surfaces stokes-theorem
differential-forms complex-geometry complex-integration riemann-surfaces stokes-theorem
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
asked Dec 8 '18 at 0:26
Sebastian H. MartensenSebastian H. Martensen
112
112
add a comment |
add a comment |
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