On the number of solutions to the discrete two-dimensional L0-Minkowski problem

By Alina Stancu. 2003

237 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/dfc97007c9634a4686d207bcea5ab319e2592da0

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

The dual Minkowski problem for symmetric convex bodies (2017, methodology): “[48] A. Stancu, The discrete planar L0-Minkowski problem, Adv.”
The Minkowski problem in Gaussian probability space (2020, background): “Due to limit of space, we mention only a selection of beautiful results in this area, [10,12,33,34,54,56,60,61,63,65, 69,70,72] and refer the interested readers to Schneider’s book [66] for more details.”
Cone-volume measure of general centered convex bodies (2016, unknown): “Stancu [40,41].”
Shadow systems of asymmetric Lp zonotopes (2013, unknown): “[9,12,21,23,26–30,32,35–37,44,46–48,51]).”
More on logarithmic sums of convex bodies (2014, background): “In [5], a necessary and sufficient condition was discovered (the planar case was treated by Stancu [42] [43]; see also [6] for other applications of the cone-volume measure and [8] for a possible functional generalization of the classical Minkowski problem).”
Dar’s conjecture and the log–Brunn–Minkowski inequality (2016, background): “5), equivalently to say, the uniqueness of the logarithmic Minkowski problem, see [5, 6, 35, 36] for details.”
The Dual Orlicz–Minkowski Problem (2017, methodology): “inkowski 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 (see e.g., [2, 4, 42, 43, 44, 60]). Note that solutions to the Lp Minkowski problem are the key ingredients in ”
General affine surface areas (2009, background): “During the past decade and a half, there has been an explosive growth of an Lp extension of the classical Brunn Minkowski theory (see, for example, [6], [7], [20], [21], [27] – [33], [41], [42]).”
A classification of $\operatorname{SL}(n)$ invariant valuations (2010, unknown): “For p > 1, Lp affine surface area was defined by Lutwak [39] as the notion corresponding to affine surface area in the Lp Brunn Minkowski theory (see [13], [14], [38] – [46], [57], [58] for”
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].”
The Spherical Convex Floating Body (2014, unknown): “Affine surface area is among the most powerful tools in equiaffine differential geometry (see B. Andrews [5] [6], A. Stancu [75] [76], M. Ivaki [32] and M. Ivaki and A. Stancu [33]).”
The log-Brunn-Minkowski inequality (2012, background): “When the convex bodies are polytopes the theorem is due to Stancu [65].”