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Award ID contains: 2104988

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  1. ; (, Journal of Mathematical Analysis and Applications)
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  2. ; (, The Journal of Geometric Analysis)
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  3. ; ; (, Commentarii Mathematici Helvetici)
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  4. ; ; (, Annals of Global Analysis and Geometry)
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  5. ; (, Pacific journal of mathematics)
    In this paper, we study closed four-dimensional manifolds. In particular, we show that under various pinching curvature conditions (for example, the sectional curvature is no more than 5 6 of the smallest Ricci eigenvalue), the manifold is definite. If restricting to a metric with harmonic Weyl tensor, then it must be self-dual or anti-self-dual under the same conditions. Similarly, if restricting to an Einstein metric, then it must be either the complex projective space with its Fubini-Study metric, the round sphere, or their quotients. Furthermore, we also classify Einstein manifolds with positive intersection form and an upper bound on the sectional curvature. 
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  6. ; ; (, Proceedings of the American Mathematical Society)
    In this paper, we study the first eigenvalue of the Jacobi operator on an integral n-varifold with constant mean curvature in the unit sphere Sn+1. We found the optimal upper bound and prove a rigidity result characterizing the case when it is attained. This gives a new characterization for certain singular Clifford tori. 
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