Rotationally symmetric solutions to the Lp-Minkowski problem

A flow approach to the Musielak-Orlicz-Gauss image problem

“…The past few years have witnessed the great progress on the Minkowski type problems and new Minkowski type problems are continuously emerging, including for example the L p Minkowski problem [43], the Orlicz-Minkowski problem [28], the dual Minkowski [32], the L p dual Minkowski [47], the dual Orlicz-Minkowski problems [25,26,56,60], and the (L p and Orlicz) Aleksandrov problem [22,33]. There is a growing body work to these problems and we only name a few [3,4,5,10,16,17,18,21,30,34,35,41,44,57,58]. The list is far from complete and more can be found in the references in, e.g., [31,32,33,60].…”

The $L_p$ Gauss image problem

“…In the early 1900's, K + p t • L can be defined for negative t if |t| is sufficient small. Lutwak [36] showed the variational formula…”

“…The L 0 Gauss image problem is just the Gauss image problem which was first mentioned in [5], and the existence of smooth solution for the Gauss image problem was in [14]. It is necessary to contrast the L p Gauss image problem with the various Minkowski problems and dual Minkowski problems that have been extensively studied, see [8,11,15,16,27,29,30,34,35,36,37,38,40,44,45] for the L p -Minkowski problem, [7,21,23,24,32,42,43] for the dual Minkowski problem, [6,9,10,25,26,31,39] for the L p dual Minkowski problem, [4,20,22,28] for the Orlicz Minkowski problem, [12,13,18,19,33] for the dual Orlicz Minkowski problem, [17] for the Orlicz Aleskandrov problem.…”

The discrete logarithmic Minkowski problem for the electrostatic $\mathfrak{p}$-capacity

“…Both the classical Minkowski problem and the logarithmic Minkowski problem are incorporated in L p Minkowski problem. The L p Minkowski problem was initiated by Lutwak in [17] for p ≥ 1 and has been intensively studied in, e.g., [7,9,12,13,15,16,18,19,20,25,29].…”