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2017

Riemannian and Lorentzian flow-cut theorems

Headrick, Matthew, Hubeny, Veronika E.

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We prove several geometric theorems using tools from the theory of convex optimization.

In the Riemannian setting, we prove the max flow-min cut theorem for boundary regions, applied recently to develop a "bit-thread" interpretation of holographic entanglement entropies.
We also prove various properties of the max flow and min cut, including respective nesting properties.
In the Lorentzian setting, we prove the analogous min flow-max cut theorem, which states that the volume of a maximal slice equals the flux of a minimal flow, where a flow is defined as a divergenceless timelike vector field with norm at least 1.

Riemannian and Lorentzian flow-cut theorems · Around

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[Online; accessed 6-September-2017 ]

Wikipedia, Max-flow min-cut theorem — wikipedia, the free encyclopedia · 2017

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