Cabezas Moreno, C., & Hu, J. (2025). The Lₚ dual Christoffel-Minkowski problem for 1 < p < q ≤ k + 1 with 1 ≤ k ≤ n. Calculus of Variations and Partial Differential Equations, 64(7), Article 229. https://doi.org/10.1007/s00526-025-03115-1
In this paper, we investigate an Lₚ Christoffel-Minkowski-type problem that prescribes a class of Lₚ geometric measures, which are mixtures of the k-th area measure and the q-th dual curvature measure. By establishing a gradient estimate, we obtain the existence of an even, smooth, strictly convex solution to this problem for 1<p<q≤k+1, where 1≤k≤n and n≥1.
