Geodesics and generalized geodesics
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Statement of Theorem
- Theorem.(Benamow-Brenier)[1] Let ,
Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle w_{2}^{2}(\mu, \nu)=\inf_{(\mu(t).\nu(t))}{\int_{0}^{1}} |v(,t)|_{L^{2}(\mu(t))}^{2}dt, \quad \partial_{t}\mu+\nabla(v\mu)=0, \mu(0)=\mu, \mu(1)=\nu} }