On solvability of two-dimensional Lp-Minkowski problem

By Vladimir Umanskiy. 2003

91 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/cdc962b84044acceecfcb1c2cf461b779d8d65c3

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In Applied Mathematics

Citations in the corpus

The even Orlicz-Minkowski problem (2010, methodology): “[1–5, 7–10, 12, 13, 15–22, 25–39, 41–44, 47, 49, 50, 52–55, 58, 60–63, 65–68]).”
The Dual Orlicz–Minkowski Problem (2017, background): “ent back to Minkowski [37, 38]. The Lp Minkowski problem was ﬁrst posed by Lutwak [30]. Since then, the Lp Minkowski problem attracted a lot of attention and amazing progress has been made (see e.g., [5, 6, 18, 21, 22, 33, 45, 61, 62, 63]). When p= 0, it becomes the logarithmic Minkowski problem (se”
A volume inequality for polar bodies (2010, unknown): “, [8–13, 15, 21–38, 41, 44,45,47–49,51]).”
The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, background): “ 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”
On the planar dual Minkowski problem (2018, background): “There is a vast body of literature concerning the planar Lp-Minkowski problem [1, 3, 5, 15, 18, 19, 20, 21, 48, 49, 50].”
Remarks on the 2-Dimensional Lp-Minkowski Problem (2010, background): “The case g > 0 and p > 2 was studied in [14], that of g > 0, p ̸= 0, 2 and T < 1 was discussed in [21], part 1 if −2 ≤ p ≤ 0, the parts 2 and 3 of Theorem 1.”
Volume inequalities for isotropic measures (2006, background): “, [7]–[11], [13]–[32], [34], [35], [37]) none of the machinery of the theory is used.”
Rotationally symmetric solutions to the L p -Minkowski problem (2013, methodology): “Sufficient conditions for the existence of solutions have been found in [1,7,11,13,20] by different methods.”
Volume Inequalities for Subspaces of L p (2004, unknown): “[7], [8], [9], [15], [16], [17], [22], [23], [24], [25], [26], [27], [28], [30], [29], [31], [32], [33], [34], [35], [39], [43], [44], [45], [46], [48]) motivated the search for a direct approach to establishing these reverse inequalities.”
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 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].”