| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
|---|
| Research Abstract |
On singular spaces admitting no differentiable structure, we identify two different formulations of heat flows as gradient flows. As a result, we prove an implication from a formulation of the presence of a lower Ricci curvature bound via optimal transport to another one via the gradient estimate of heat semigroups.
By using stochastic analytic techniques, we extend an estimate of the Wasserstein distance between heat distributions which appears as a kind of curvature condition in the above argument to the one on Ricci flows. In addition, we extend it to the one associated with the Wasserstein-like distance defined by using Perelman's L-distance.
We obtain a formulation of a characteristic property of the mirror coupling in terms of optimal transport. By using this formulation, we proved that the same property holds on a class of singular spaces given by limit of Riemannian manifolds.
|
