Any closed hypersurface has at least one point where all curvatures are positive
$begingroup$
Any closed hypersurface has at least one point where all curvatures are positive.
How to prove this statement?
I found that statement at the paper "
Volume-preserving flow by powers of the mth mean curvature"
I don't have any idea... they said it's like a trivial one.
differential-geometry
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
$endgroup$
add a comment |
$begingroup$
Any closed hypersurface has at least one point where all curvatures are positive.
How to prove this statement?
I found that statement at the paper "
Volume-preserving flow by powers of the mth mean curvature"
I don't have any idea... they said it's like a trivial one.
differential-geometry
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
$endgroup$
$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07
add a comment |
$begingroup$
Any closed hypersurface has at least one point where all curvatures are positive.
How to prove this statement?
I found that statement at the paper "
Volume-preserving flow by powers of the mth mean curvature"
I don't have any idea... they said it's like a trivial one.
differential-geometry
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
$endgroup$
Any closed hypersurface has at least one point where all curvatures are positive.
How to prove this statement?
I found that statement at the paper "
Volume-preserving flow by powers of the mth mean curvature"
I don't have any idea... they said it's like a trivial one.
differential-geometry
differential-geometry
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
asked Dec 8 '18 at 5:18
boytaehunboytaehun
111
111
$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07
add a comment |
$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07
$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07
add a comment |
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$begingroup$
from the orthogonality we can say at least one point per dimension where curvature is positive. But all at one point?
$endgroup$
– John L Winters
Dec 8 '18 at 5:25
$begingroup$
Yes! The title is exact statement from the paper.
$endgroup$
– boytaehun
Dec 8 '18 at 13:07