On LYZ's conjecture for the U-functional

Affine Subspace Concentration Conditions for Centered Polytopes

“…We are, however, able to treat the equality case in two special cases: As a byproduct of the proof of Theorem 1.2, we will see alternative proofs of (1.2) in these special cases. The first case of Theorem 1.2 slightly generalizes a former result by Zhou and He [20,Thm. 1.2].…”

Affine subspace concentration conditions for centered polytopes

“…As a byproduct of the proof of Theorem 1.2, we will see alternative proofs of (1.2) in these special cases. The first case of Theorem 1.2 slightly generalizes a former result by Zhou and He [20,Theorem 1.2]. There an additional technical assumption on 𝑃 is made.…”

The dual Orlicz-Aleksandrov-Fenchel inequality

“…L p addition and inequalities are the fundamental and core content in the L p Brunn-Minkowski theory. For recent important results and more information from this theory, we refer to x [16] [20][21][22][23], [29], [31], [35][36][37][38][39], [42][43], [48][49], [51][52], x [59] and the references therein.…”