| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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)
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| Outline of Final Research Achievements |
We proved the differential Harnack inequality for the geometric flow in abstract setting. As a corollary, we obtained a new differential Harnack inequality for positive solutions to the conjugate heat equations associated with the Ricci flow coupled with harmonic map heat flow. We also proved a new differential Harnack inequality for the Ricci Yang-Mills flow on surface. Moreover, we introduced a reduced volume type quantity for the Ricci Yang-Mills flow on surface and proved its monotonicity under the flow. Under a mild condition on the curvature,we also proved a Perelman type no local collapsing theorem for the Ricci Yang-Mills flow in general dimension.
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