On the planar dual Minkowski problem
In this paper, we resolve the planar dual Minkowski problem, proposed by Huang et al. (2016)  for all positive indices without any symmetry assumption. More precisely, given any , and function f on , bounded by two positive constants, we show that there exists a convex body Ω in the plane, containing the origin in its interior, whose dual curvature measure has density f. In particular, if f is smooth, then ∂Ω is also smooth.
|Collections||ANU Research Publications|
|Source:||Advances in Mathematics|
|01_Chen_On_the_planar_dual_Minkowski_2018.pdf||622.5 kB||Adobe PDF||Request a copy|
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