The even Orlicz-Minkowski problem

By Christoph Haberl, Erwin Lutwak, Deane Yang, Gaoyong Zhang. 2010

355 citations recorded by the source corpus.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/5fb3751cb246396ca68c089b2de0c7a9525cc587

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In Applied Mathematics

In Geometry and Topology

Citations in the corpus

The Minkowski problem in Gaussian probability space (2020, methodology): “Inspired by their work, particularly the work [31] by Haberl-LutwakYang-Zhang, we obtain the following normalized solution to the even Gaussian Minkowski problem.”
R\'enyi Divergence and $L_p$-affine surface area for convex bodies (2011, neutral): “, [5], [7] - [11], [13], [14], [17] - [24], [26], [28], [31] - [34], [37], [38] - [46], [50]), is now a central part of modern convex geometry.”
THE ORLICZ-BRUNN-MINKOWSKI THEORY: A GENERAL FRAMEWORK, ADDITIONS, AND INEQUALITIES (2013, background): “So far only a few other articles advance the theory, among which we mention [11] and [16], which address the Orlicz version of the Minkowski problem.”
A flow method for the dual Orlicz–Minkowski problem (2020, background): “The equation of the Orlicz-Minkowski problem also contains a constant c which is not equal to 1 in general, see [26, 30, 38].”
A new proof of the Orlicz Busemann-Petty centroid inequality (2011, background): “Recently, in three remarkable papers [12, 23, 24], an Orlicz Brunn-Minkowski theory which extends the Lp Brunn-Minkowski theory emerged.”
The log-Brunn-Minkowski inequality (2012, neutral): “[5,8–12,16,18,22–30,32–55,58,62–65,67–69]).”
The Centro-Affine Hadwiger Theorem (2013, background): “ies strengthen and directly imply their classical predecessors. Recently, the next step in the evolution of the Brunn-Minkowski theory towards an Orlicz Brunn-Minkowski theory has been made (see e.g. [27,42,47,57,58]). The functionals Ωϕ from 2 Theorem 1.2 constitute far reaching generalizations of ”
The logarithmic Minkowski problem (2012, positive): “Extensions of the L p -Minkowski problem are studied in [24].”
Local $L^p$-Brunn-Minkowski inequalities for $p<1$ (2017, background): “Lutwak [42, 43], leading to a rich theory with many parallels to the classical one (see also [25] and the references therein for further extensions to more general Orlicz norms).”
Orlicz–John ellipsoids (2014, background): “Beginning with the ground-breaking articles of Lutwak, Yang, Zhang and Harbel [22,39,40], a more wide extension of the Lp Brunn–Minkowski theory, called the Orlicz Brunn–Minkowski theory, emerged out three years ago.”
On the L dual Minkowski problem (2018, methodology): “Setting q = n, the following theorem contains the solution to the even Lp Minkowski problem when p > 0 and p ∕= n which was obtained in Lutwak [49] and Haberl, Lutwak, Yang & Zhang [27].”
Dual Orlicz-Brunn-Minkowski theory (2014, positive): “This theory is far more general than the Lp Brunn–Minkowski theory, we refer the reader to [6,16,24,26,29,32,40,43,44,46,53, 57].”
The dual Orlicz–Brunn–Minkowski theory ☆ (2014, background): “) The new theory has already attracted considerable interest; see, for example, [2, 3, 4, 5, 21, 22, 25, 26, 39, 40, 41, 46].”
The p-capacitary Orlicz–Hadamard variational formula and Orlicz–Minkowski problems (2017, methodology): “Similar arguments for the volume can be found in [16, 18].”