The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry

By Kai-Seng Chou, Xu-jia Wang. 2006

214 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/d2a5dd5cfdac584879a84c90784b8fae1dadc41f

Citations in the corpus

• 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 for polytopes (2014, unknown): “In [13], Chou and Wang treated the logarithmic Minkowski problem for the case where the measure has a positive density.”
• On the L dual Minkowski problem (2018, unknown): “It is worth noting that the Lp dual Minkowski problem contains the classical Minkowski problem and the Aleksandrov problem, as well as the unsolved logarithmic Minkowski problem [10, 70] and the unsolved centro-affine Minkowski problem [19, 71].”
• 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], and [58] for contributions to the Lp Brunn Minkowski theory).”
• Orlicz projection bodies (2010, unknown): “[2–8,14–19,22–28,30–43,49,51, 52,54,55].”
• Lp John Ellipsoids (2005, unknown): “If in addition to containing the origin in its interior, the body K has a curvature function, then fpðK; Þ:S 1 ! R, the Lp-curvature function of K, is de2ned by fpðK; Þ 1⁄4 h(1) p K fðK; Þ: Since its introduction in the mid 90 s, Lp curvature (and the functionals it gives rise to) have attracted inc”
• The dual Minkowski problem for negative indices (2017, unknown): “See also Chou & Wang [12] for the case when the given measure has a positive density.”
• On the Christoffel-Minkowski problem of Firey’s p-sum (2004, unknown): “So it is natural to consider a generalization of the classical Christofiel-Minkowski problem for each p > 1. The generalized Minkowski problem has been treated in [13, 15, 7, 4 ]. In this paper we study the remaining case, which may be called the Christofiel-Minkowski problem of p-sum.”
• Valuations and Busemann{Petty Type Problems (2008, unknown): “[9,10,44–47].”
• The discrete logarithmic Minkowski problem (2014, unknown): “[14] K.-S. Chou, X.-J. Wang, The Lp-Minkowski problem and the Minkowski problem in centroaffine geometry.”
• Existence of solutions to the even dual Minkowski problem (2018, unknown): “The characterization problem, in this case, is the centro-affine Minkowski problem posed in Chou & Wang [14].”
• Rotationally symmetric solutions to the L p -Minkowski problem (2013, unknown): “The above existence was proved in [9] for general function f .”