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Award ID contains: 1749447

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  1. ; (, Advances in Mathematics)
    We extend Prekopa’s Theorem and the Brunn-Minkowski Theo- rem from convexity to F-subharmonicity. We apply this to the interpolation problem of convex functions and convex sets introducing a new notion of “har- monic interpolation” that we view as a generalization of Minkowski-addition. 
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  2. (, Birational Geometry, Kähler–Einstein Metrics and Degenerations)
    Ivan Cheltsov, Xiuxiong Chen (Ed.)
    We prove that Schur classes of nef vector bundles are limits of classes that have a property analogous to the Hodge-Riemann bilinear relations. We give a number of applications, including (1) new log-concavity statements about characteristic classes of nef vector bundles (2) log-concavity statements about Schur and related polynomials (3) another proof that normalized Schur polynomials are Lorentzian. 
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    Accepted Manuscript Full Text Available
  3. ; (, International Mathematics Research Notices)
    We prove a version of the Hodge–Riemann bilinear relations for Schur polynomials of Kähler forms and for Schur polynomials of positive forms on a complex vector space. 
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  4. ; (, The Journal of Geometric Analysis)
    Full Text Available 
  5. ; (, Pure and applied mathematics quarterly)
    null; Tosatti, Valentino; Weinkove, Ben (Ed.)
    We prove an existence result for twisted Kähler–Einstein metrics, assuming an appropriate twisted K‑stability condition. An improvement over earlier results is that certain non-negative twisting forms are allowed. 
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    Accepted Manuscript Full Text Available
  6. ; (, Journal of convex analysis)
    Suppose $$f(x,y) + \frac{\kappa}{2} \|x\|^2 - \frac{\sigma}{2}\|y\|^2$$ is convex where $$\kappa\ge 0, \sigma>0$$, and the argmin function $$\gamma(x) = \{ \gamma : \inf_y f(x,y) = f(x,\gamma)\}$$ exists and is single valued. We will prove $$\gamma$$ is differentiable almost everywhere. As an application we deduce a minimum principle for certain semiconcave subsolutions. 
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    Accepted Manuscript Full Text Available