Lp Minkowski problem with not necessarily positive data

By Wenxiong CHEN *. 2006

149 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/580d805b14f06e6f28821a5a646a75bab7444be7

Citations in the corpus

• The even Orlicz-Minkowski problem (2010, unknown): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”
• Rotationally symmetric solutions to the L p -Minkowski problem (2013, unknown): “Sufficient conditions for the existence of solutions have been found in [1,7,11,13,20] by different methods.”
• Relative entropy of cone measures and Lp centroid bodies (2009, unknown): “…Pajor [42] that if K is a symmetric convex body, then, for large δ, the floating body Kδ is always uniformly, up to a factor c(δ) depending on δ, isomorphic to the dual of the Binet ellipsoid from classical mechanics and consequently K◦δ is isomorphic (up to a factor c(δ)) to the Binet ellipsoid.”
• Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems (2016, unknown): “, [18], [20], [43], [44], [54], [55], and [84].”
• On the planar dual Minkowski problem (2018, unknown): “There is a vast body of literature concerning the planar Lp-Minkowski problem [1, 3, 5, 15, 18, 19, 20, 21, 48, 49, 50].”
• Existence of solutions to the even dual Minkowski problem (2018, unknown): “Important contributions towards the regularity of the solution to the Minkowski problem include Caffarelli [11], Cheng & Yau [13], Nirenberg [49], etc.”
• The logarithmic Minkowski problem (2012, unknown): “In the plane ( n = 2), the L p -Minkowski problem was treated by Stancu [57,58], Uman-skiy [61], Chen [7], and by Jiang [32].”
• Remarks on the 2-Dimensional Lp-Minkowski Problem (2010, unknown): “These results complement and generalize those in [1,5,14,21].”
• Sharp convex Lorentz–Sobolev inequalities (2011, unknown): “Within the Lp Brunn-Minkowski theory (see [10,13–15,30–32,35,36,39–42,44–49,61,67,69– 71, 74]), the natural extension of integral affine surface area is the Lp integral affine surface area Φp (see Section 5.”
• The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, unknown): “ interior). Its Lq extension, namely the Lq Minkowski problem [31], has been a central object of interest in convex geometric analysis for decades and has received extensive considerations (see e.g., [9, 10, 21, 23, 32, 41, 50, 51, 52]). Both the classical and Lq Minkowski problems are related to fu”
• The dual Minkowski problem for negative indices (2017, unknown): “See also Chen [11], Lutwak [31], LYZ [35], and Zhu [51].”