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  1. ; ; (, The Journal of Geometric Analysis)
    Abstract An affine Pólya-Szegö principle for a family of affine energies, with equality condition characterization, is demonstrated. In particular, this recovers, as special cases, the$$L^p$$ L p affine Pólya-Szegö principles due to Cianchi, Lutwak, Yang and Zhang, and subsequently Haberl, Schuster and Xiao. Various applications of this new Pólya-Szegö principle are shown. 
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  2. ; (, Transactions of the American Mathematical Society)
    The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Ampère equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and sufficient condition for existence and uniqueness) in dimension 2 is presented. In higher dimensions, partial results are demonstrated. 
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    Free, publicly-accessible full text available May 29, 2026
  3. ; ; ; (, Calculus of Variations and Partial Differential Equations)
    Free, publicly-accessible full text available March 1, 2026