Existence of smooth convex capillary bodies with prescribed capillary L_p-surface area measure is proved for all p>1, with a symmetry condition needed when 1<p<n+1.
Self-similar solutions for the anisotropic affine curve shortening problem
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The capillary $L_p$-Minkowski problem
Existence of smooth convex capillary bodies with prescribed capillary L_p-surface area measure is proved for all p>1, with a symmetry condition needed when 1<p<n+1.