The <i>L</i> <sub> <i>p</i> </sub> chord Minkowski problem
نویسندگان
چکیده
Abstract Chord measures are newly discovered translation-invariant geometric of convex bodies in R n {{\mathbb{R}}}^{n} , addition to Aleksandrov-Fenchel-Jessen’s area measures. They constructed from chord integrals and random lines. Prescribing the L p {L}_{p} is called Minkowski problem Brunn-Minkowski theory, which includes as a special case. This article solves when > 1 p\gt 1 symmetric case 0 < 0\lt p\lt .
منابع مشابه
The regularity problem for sub-Riemannian geodesics
One of the main open problems in sub-Riemannian geometry is the regularity of length minimizing curves, see [12, Problem 10.1]. All known examples of length minimizing curves are smooth. On the other hand, there is no regularity theory of a general character for sub-Riemannian geodesics. It was originally claimed by Strichartz in [15] that length minimizing curves are smooth, all of them being ...
متن کاملAlgorithms for the Densest Sub-Lattice Problem
We give algorithms for computing the densest k-dimensional sublattice of an arbitrary lattice, and related problems. This is an important problem in the algorithmic geometry of numbers that includes as special cases Rankin’s problem (which corresponds to the densest sublattice problem with respect to the Euclidean norm, and has applications to the design of lattice reduction algorithms), and th...
متن کاملThe Regularity Problem for Sub-riemannian Geodesics
We study the regularity problem for sub-Riemannian geodesics, i.e., for those curves that minimize length among all curves joining two fixed endpoints and whose derivatives are tangent to a given, smooth distribution of planes with constant rank. We review necessary conditions for optimality and we introduce extremals and the Goh condition. The regularity problem is nontrivial due to the presen...
متن کاملElectrochemical Stability of Li<sub>10</sub>GeP<sub>2</sub>S<sub>12</sub> and Li<sub>7</sub>La<sub>3</sub>Zr<sub>2</sub>O<sub>12</sub> Solid Electrolytes
DOI: 10.1002/aenm.201501590 electrochemical stability window, and (3) chemical compatibility with the anode and cathode. In the past few years, major advances have been achieved in increasing the Li ionic conductivity of the solid electrolytes. The state-of-the-art solid electrolyte materials, such as Li-garnet Li 7 La 3 Zr 2 O 12 (LLZO) and Li 10 GeP 2 S 12 (LGPS) have achieved an ionic conduc...
متن کاملMagnetic properties of the Haldane-gap material [Ni(C<sub>2</sub>H<sub>8</sub>N<sub>2</sub>)<sub>2</sub>NO<sub>2</sub>](BF<sub>4</sub>)
Results of magnetization and high-field electron spin resonance (ESR) studies of the new spin-1 Haldane-chain material [Ni(C2H8N2)2NO2] (BF4) (NENB) are reported. A definite signature of the Haldane state in NENB was obtained. From the analysis of the frequency–field dependence of magnetic excitations in NENB, the spin-Hamiltonian parameters were calculated, yielding 1/kB = 17.4 K, g‖ = 2.14, D...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Advanced Nonlinear Studies
سال: 2023
ISSN: ['1536-1365', '2169-0375']
DOI: https://doi.org/10.1515/ans-2022-0041