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Decomposition of an integrally convex set into a Minkowski sum of bounded and conic integrally convex sets
Every polyhedron can be decomposed into a Minkowski sum (or vector sum) of a bounded polyhedron and a polyhedral cone. This paper establishes similar...
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The time-like minimal surface equation in Minkowski space: low regularity solutions
It has long been conjectured that for nonlinear wave equations that satisfy a nonlinear form of the null condition, the low regularity well-posedness...
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The Logarithmic Capacitary Minkowski Problem for Polytopes
The logarithmic capacitary Minkowski problem asks for necessary and sufficient conditions on a finite Borel measure on the unit sphere so that it is...
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The General Dual-Polar Orlicz–Minkowski Problem
This paper gives a systematic study to the general dual-polar Orlicz–Minkowski problem (e.g., Problem 4.1). This problem involves the general dual...
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Minkowski Geometry—Some Concepts and Recent Developments
The geometry of finite-dimensional normed spaces (= Minkowski geometry) is a research topic which is related to many other fields, such as convex...
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Multiplicity and Calabi–Bernstein type asymptotic property of positive solutions for one-dimensional Minkowski-curvature problems
In this paper, we first consider the existence and multiplicity of positive solutions to a Minkowski-curvature problem when nonlinearity is...
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A Note on Borsuk’s Problem in Minkowski Spaces
AbstractIn 1993, Kahn and Kalai famously constructed a sequence of finite sets in d -dimensional Euclidean spaces that cannot be partitioned into...
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Multiple Positive Periodic Solutions to Minkowski-Curvature Equations with a Singularity of Attractive Type
Using Leray–Schauder degree theory, we investigate the existence and multiplicity of positive T -periodic solutions to Minkowski-curvature equations...
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Existence of Smooth Even Solutions to the Dual Orlicz–Minkowski Problem
In this paper, we study the dual Orlicz–Minkowski problem, which is a generalization of the dual Minkowski problem in convex geometry. By considering...
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On the existence of solutions to the Orlicz–Minkowski problem for torsional rigidity
In [J Diff Equ, 269: 8549–8572, 2020], Li and Zhu studied the Orlicz–Minkowski problem for torsional rigidity, and among other things, they proved...
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A generic functional inequality and Riccati pairs: an alternative approach to Hardy-type inequalities
We present a generic functional inequality on Riemannian manifolds, both in additive and multiplicative forms, that produces well known and genuinely...
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Stability of the Gaussian Faber–Krahn inequality
We prove a quantitative version of the Gaussian Faber–Krahn type inequality proved in (Betta et al. in Z. Angew. Math. Phys. 58:37–52, 2007) for the...
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On a Brunn–Minkowski inequality for measures with quasi-convex densities
In this paper we prove that the classical Brunn–Minkowski inequality holds for product measures on the Euclidean space with quasi-convex densities...
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Littlewood-Paley Theorem, Nikolskii Inequality, Besov Spaces, Fourier and Spectral Multipliers on Graded Lie Groups
In this paper we investigate Besov spaces on graded Lie groups. We prove a Nikolskii type inequality (or the Reverse Hölder inequality) on graded Lie...