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京东 11.11 红包
Anusha Krishnan:Positive sectional curvature and Ricci flow
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https://www.youtube.com/watch?v=obG_9utb9wk Virtual Seminar on Geometry with Symmetries Anusha Krishnan (University of Münster)-Positive sectional curvature and Ricci flow The preservation of positive curvature conditions under the Ricci flow has been an important ingredient in applications of the flow to solving problems in geometry and topology. Works by Hamilton and others established that certain positive curvature conditions are preserved under the flow, culminating in Wilking's unified, Lie algebraic approach to proving invariance of positive curvature conditions. Yet, some questions remain. In this talk, we describe positively curved metrics on $S^4$ and $\mathbb{C}P^2$, which evolve under the Ricci flow to metrics with sectional curvature of mixed sign. The setting is that of metrics invariant under a Lie group action of cohomogeneity one. This is joint work with Renato Bettiol. Anusha M. Krishnan Homepage:https://www.uni-muenster.de/IVV5WS/WebHop/user/akrishna/ Renato G. Bettiol, Anusha M. Krishnan——《Four-dimensional cohomogeneity one Ricci flow and nonnegative sectional curvature》:https://doi.org/10.48550/arXiv.1606.00778 We exhibit the first examples of closed 4-manifolds with nonnegative sectional curvature that lose this property when evolved via Ricci flow. Renato G. Bettiol, Anusha M. Krishnan——《Ricci flow does not preserve positive sectional curvature in dimension four》:https://doi.org/10.48550/arXiv.2112.13291 We find examples of cohomogeneity one metrics on S4 and CP2 with positive sectional curvature that lose this property when evolved via Ricci flow. These metrics are arbitrarily small perturbations of Grove--Ziller metrics with flat planes that become instantly negatively curved under Ricci flow. Wolfgang Ziller Homepage:https://www2.math.upenn.edu/~wziller/
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