2011 Fiscal Year Final Research Report
Geometric Analysis on non-compact spaces and the geometry of infinite dimensional moduli spaces
| Project/Area Number |
21740048
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Geometry
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| Research Institution | Kyoto University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | 微分幾何 / 複素解析 / 力学系 |
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| Research Abstract |
I concentrate on the most important results. I constructed an example of oriented complete Riemannian 4-manifolds having no non-trivial instanton. We studied moduli spaces of ASD connections whose curvatures are uniformly bounded over the product space of 3-sphere and the line. We got an estimate relating their local mean dimension to the energy densities of connections. We got an estimate relating a mean dimension of the space of Brody curves to the energy densities of curves. In particular we got an exact formula which represents the mean dimension by using the energy densities in the case that the target space is the Riemann sphere.
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