The $L_p$-Aleksandrov problem for $L_p$-integral curvature
By Yong Huang, Erwin Lutwak, Deane Yang, Gaoyong Zhang. Journal of differential geometry, 2018
87 citations recorded by the source corpus.
It is shown that within the Lp-Brunn–Minkowski theory that Aleksandrov’s integral curvature has a natural Lp extension, for all real p. This raises the question of finding necessary and sufficient conditions on a given measure in order for it to be the Lp-integral curvature of a convex body. This problem is solved for positive p and is answered for negative p provided the given measure is even.
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/047df612327069e070de30eb578c6aa5296e8c09
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In Applied Mathematics
In Geometry and Topology
Citations in the corpus
- The Lp dual Minkowski problem and related parabolic flows (2021, background): “The Lp dual curvature measures include some fundamental geometric measures in the Brunn-Minkowski theory and its dual theory of convex bodies as special cases, such as the Lp surface area measures [39], the dual curvature measures [33] and the Lp-integral curvatures [34], and therefore extend the cl”