| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We consider two generalizations of the curvature-dimension condition, which is a notion of a lower Ricci curvature bound for metric measure spaces. One generalization is to make the parameter regarded as an “upper bound of the dimension” being negative. Then the condition is getting weaker and covers a wider class of spaces.
We also establish the Bochner formula for Finsler manifolds by using the weighted Ricci curvature. As applications, we obtain some gradient estimates for heat flow, and a generalization of Cheeger-Gromoll’s classical splitting theorem.
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