The $${\varphi}$$φ-Brunn–Minkowski inequality
Sign Up to like & getrecommendations! Published in 2018 at "Acta Mathematica Hungarica"
DOI: 10.1007/s10474-018-0825-8
Abstract: For strictly increasing concave functions $${\varphi}$$φ whose inverse functions are log-concave, the $${\varphi}$$φ-Brunn–Minkowski inequality for planar convex bodies is established. It is shown that for convex bodies in $${\mathbb{R}^n}$$Rn the $${\varphi}$$φ-Brunn–Minkowski is equivalent to the… read more here.
Keywords: varphi brunn; minkowski inequality; brunn minkowski;
The Brunn–Minkowski inequality for the principal eigenvalue of fully nonlinear homogeneous elliptic operators
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2019.106855
Abstract: Abstract We prove that the principal eigenvalue of any fully nonlinear homogeneous elliptic operator which fulfills a very simple convexity assumption satisfies a Brunn-Minkowski type inequality on the class of open bounded sets in R… read more here.
Keywords: fully nonlinear; nonlinear homogeneous; brunn minkowski; eigenvalue fully ... See more keywords
Brunn-Minkowski type inequalities for the lattice point enumerator
Sign Up to like & getrecommendations! Published in 2020 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2020.107193
Abstract: Geometric and functional Brunn-Minkowski type inequalities for the lattice point enumerator $\mathrm{G}_n(\cdot)$ are provided. In particular, we show that $$\mathrm{G}_n((1-\lambda)K + \lambda L + (-1,1)^n)^{1/n}\geq (1-\lambda)\mathrm{G}_n(K)^{1/n}+\lambda\mathrm{G}_n(L)^{1/n}$$ for any non-empty bounded sets $K, L\subset\mathbb{R}^n$ and all… read more here.
Keywords: brunn minkowski; type inequalities; lattice point; lambda ... See more keywords
Brunn-Minkowski inequality for $L_p$-mixed intersection bodies
Sign Up to like & getrecommendations! Published in 2017 at "Miskolc Mathematical Notes"
DOI: 10.18514/mmn.2017.416
Abstract: In this paper, we establish Lp-Brunn-Minkowski inequality for dual Quermassintegral of Lp-mixed intersection bodies. As application, we give the well-known Brunn-Minkowski inequality for mixed intersection bodies. 2010 Mathematics Subject Classification: 52A40 read more here.
Keywords: mixed intersection; intersection bodies; minkowski inequality; brunn minkowski ... See more keywords