Zero constant mean curvature in Minkowski space versus in Euclidean space
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There's a famous result in $mathbb{R}^3$ which goes as: there are no compact minimal surfaces in $mathbb{R}^3$.So the mean curvature cannot be zero in compact surfaces in $mathbb{R}^3$. Now what's the intuition behind why that isn't true in the Minkowski space $E_1^3$ (also known as $mathbb{L}^3$)?
differential-geometry riemannian-geometry semi-riemannian-geometry
asked Dec 8 '18 at 8:14
user71487user71487
948
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$begingroup$
There's a famous result in $mathbb{R}^3$ which goes as: there are no compact minimal surfaces in $mathbb{R}^3$.So the mean curvature cannot be zero in compact surfaces in $mathbb{R}^3$. Now what's the intuition behind why that isn't true in the Minkowski space $E_1^3$ (also known as $mathbb{L}^3$)?
differential-geometry riemannian-geometry semi-riemannian-geometry
asked Dec 8 '18 at 8:14
user71487user71487
948
$endgroup$
add a comment |
$begingroup$
There's a famous result in $mathbb{R}^3$ which goes as: there are no compact minimal surfaces in $mathbb{R}^3$.So the mean curvature cannot be zero in compact surfaces in $mathbb{R}^3$. Now what's the intuition behind why that isn't true in the Minkowski space $E_1^3$ (also known as $mathbb{L}^3$)?
differential-geometry riemannian-geometry semi-riemannian-geometry
asked Dec 8 '18 at 8:14
user71487user71487
948
$endgroup$
There's a famous result in $mathbb{R}^3$ which goes as: there are no compact minimal surfaces in $mathbb{R}^3$.So the mean curvature cannot be zero in compact surfaces in $mathbb{R}^3$. Now what's the intuition behind why that isn't true in the Minkowski space $E_1^3$ (also known as $mathbb{L}^3$)?
differential-geometry riemannian-geometry semi-riemannian-geometry
differential-geometry riemannian-geometry semi-riemannian-geometry
asked Dec 8 '18 at 8:14
user71487user71487
948
asked Dec 8 '18 at 8:14
user71487user71487
948
asked Dec 8 '18 at 8:14
user71487user71487
948
asked Dec 8 '18 at 8:14
user71487user71487
948
asked Dec 8 '18 at 8:14
user71487user71487
948
948
add a comment |
add a comment |
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