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A random mathematician
A random mathematician
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Let $\Omega \subset R^3$ be a bounded open region. It is well known that there exists a smooth surface $\Gamma$ with minimum area and constant mean curvature which is orthogonal to $\partial \Omega$ and divides $\Omega$ into two regions of equal volume. I wonder if there is a numerical algorithm for constructing such $\Gamma$.

Let $\Omega \subset R^3$ be a bounded open region. It is well known that there exists a smooth surface $\Gamma$ with constant mean curvature which is orthogonal to $\partial \Omega$ and divides $\Omega$ into two regions of equal volume. I wonder if there is a numerical algorithm for constructing such $\Gamma$.

Let $\Omega \subset R^3$ be a bounded open region. It is well known that there exists a smooth surface $\Gamma$ with minimum area and constant mean curvature which is orthogonal to $\partial \Omega$ and divides $\Omega$ into two regions of equal volume. I wonder if there is a numerical algorithm for constructing such $\Gamma$.

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A random mathematician
A random mathematician
  • 773
  • 5
  • 19

Convergent algorithm for dividing a body into two regions of equal volume

Let $\Omega \subset R^3$ be a bounded open region. It is well known that there exists a smooth surface $\Gamma$ with constant mean curvature which is orthogonal to $\partial \Omega$ and divides $\Omega$ into two regions of equal volume. I wonder if there is a numerical algorithm for constructing such $\Gamma$.