Are there closed hypersurfaces in $mathbb{R}^n$ with negative mean curvature (not necessarily constant)?
1
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Are there closed hypersurfaces in $mathbb{R}^n$ (i.e. the boundary of a bounded domain in $mathbb{R}^n$) with negative mean curvature (not necessarily constant)?
differential-geometry riemannian-geometry
asked Jan 13 at 8:40
MichealMicheal
764
$endgroup$
add a comment |
1
$begingroup$
Are there closed hypersurfaces in $mathbb{R}^n$ (i.e. the boundary of a bounded domain in $mathbb{R}^n$) with negative mean curvature (not necessarily constant)?
differential-geometry riemannian-geometry
asked Jan 13 at 8:40
MichealMicheal
764
$endgroup$
2
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03
add a comment |
1
1
1
$begingroup$
Are there closed hypersurfaces in $mathbb{R}^n$ (i.e. the boundary of a bounded domain in $mathbb{R}^n$) with negative mean curvature (not necessarily constant)?
differential-geometry riemannian-geometry
asked Jan 13 at 8:40
MichealMicheal
764
$endgroup$
Are there closed hypersurfaces in $mathbb{R}^n$ (i.e. the boundary of a bounded domain in $mathbb{R}^n$) with negative mean curvature (not necessarily constant)?
differential-geometry riemannian-geometry
differential-geometry riemannian-geometry
asked Jan 13 at 8:40
MichealMicheal
764
asked Jan 13 at 8:40
MichealMicheal
764
asked Jan 13 at 8:40
MichealMicheal
764
asked Jan 13 at 8:40
MichealMicheal
764
asked Jan 13 at 8:40
MichealMicheal
764
764
2
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03
add a comment |
2
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03
2
2
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03
add a comment |
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2
$begingroup$
Think about the shape of the hypersurface at an extreme point, i.e. a point maximizing the distance to (some choice of) the origin.
$endgroup$
– Anthony Carapetis
Jan 13 at 10:03