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On the regularity of the lp minkowski problem

WebOn the regularity of the Lp Minkowski problem - CORE Reader WebTheLp-Minkowski problem was flrst formulated and studied in Lutwak[L]. He showed that any even flnite Borel measure is ap-area measure for a unique centrally symmetric convex body. The regularity of the convex body (whenf is regular) was later established in Lutwak-Oliker[LO]. We observe that not every flnite Borel measure is ap-area function.

The Lp-Minkowski Problem and the Minkowski Problem in Centroa–ne Geometry

WebThis paper concerns the continuity of the solution to the even Lp Minkowski problem in the plane. When 0 < p < 1, ... S.-Y. Cheng and S.-T. Yau, On the regularity of the solution of the n-dimensional Minkowski problem, Comm. Pure Appl. Math. 29 (1976) 495–561. WebOn the regularity of the solution of the n-dimensional Minkowski problem. Shiu-Yuen Cheng, Princeton University. Search for more papers by this author. Shing-Tung Yau, … durham academy varsity softball https://5pointconstruction.com

On the regularity of the Lp Minkowski problem - ScienceDirect

Web1 de jan. de 1995 · In [23], Lutwak proved that the solution to the L p Minkowski problem is unique for > p 1 and ≠ p n if μ is even and positive. In [24], Lutwak and Oliker proved the regularity of the solution... Web1 de dez. de 2003 · Thus the Lp -Minkowski problem concerns the existence of a closed convex hypersurface whose reciprocal Gauss curvature is ghp−1, where h is the support … WebLp Minkowski problem for electrostatic p-capacity Du Zou1 Ge Xiong2 1. Department of Mathematics, Wuhan University of Science and Technology, Wuhan, ... Establishing the regularity of the solution to the Minkwoski problem is difficult and has led to a long series of highly influential works, see, e.g., Lewy [42], Nirenberg cryptococcus mode of transmission

The Lp-Minkowski Problem and the Minkowski Problem in Centroa–ne Geometry

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On the regularity of the lp minkowski problem

A flow approach to the planar Lp$L_p$ Minkowski problem

Web19 de jun. de 2024 · In this paper we study the Lpq -dual Minkowski problem for the case p &lt; 0 &lt; q. We prove for any positive smooth function f on \mathbb {S}^ {1}, there exists an F: ℝ + → ℝ −, such that if F ( q) &lt; p &lt; 0 or 0 &lt; q &lt; − F (− p) then there is a smooth and strictly convex body solving the planar Lpq -dual Minkowski problem. Web13 de jul. de 2024 · In this paper, we consider the \(L_p\) dual Minkowski problem by geometric variational method. Using anisotropic Gauss–Kronecker curvature flows, we establish the existence of smooth solutions of the \(L_p\) dual Minkowski problem when \(pq\ge 0\) and the given data is even. If \(f\equiv 1\), we show under some restrictions on …

On the regularity of the lp minkowski problem

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WebMinkowski problem for polytopes and applications of the Lp Minkowski problem to sharp affine in-variant Lp Sobolevinequalities [26,27]. From the view of partial differential … WebMinkowski problem (1.1), B or oczky-Lutwak-Yang-Zhang [5] obtained the existence of the even logarithmic Minkowski problem provided that the given measure satis ed the …

Web1 de jan. de 2024 · In this paper, we study the $ L_p $ dual Minkowski problem, an extension of the dual Minkowski problem. We deal with some cases in which there is no uniform estimate for the Gauss curvature... Web15 de set. de 2024 · In this paper, it is proved that the weak convergence of the Lp Gaussian surface area measures implies the convergence of the corresponding convex bodies in the Hausdorff metric for p ≥ 1. Moreover, continuity of the solution to the Lp Gaussian Minkowski problem with respect to p is obtained. Download to read the full …

Webp Brunn-Minkowski theory is the L p Minkowski problem. A solution to the L p Minkowski problem when the data is even was given in [11]. This solution turned out to be a critical ingredient in the recently established L p affine Sobolev inequality [17]. Suppose the real index p is fixed. The L p Minkowski problem for polytopes asks for the WebHoldings; Item type Current library Collection Call number Status Date due Barcode Item holds; Book Europe Campus Main Collection: Print: QA273 .D84 2002 (Browse shelf (Opens below))

WebLp-Minkowski problem (q= n). The dual Minkowski problem was first pro-posed by Huang, Lutwak, Yang and Zhang in their recent groundbreaking work [18] and then followed by [4, 15, 17, 29, 46, 47 ... durham accommodation studentWebWhile the logarithmic Minkowski problem (p = 0) and the centro-affine Minkowski problem (p = −n) are two special cases; see, e.g., [5], and [12]. The regularity of the Lp-Minkowski problem, for example [12,28,40]. In [38], the dual Brunn-Minkowski theory was developed in the 1970s. The most significant dual curvature measure and its ... durham accounting \u0026 managementWebMinkowski solved the problem in the category of polyhedrons. Then A. D. Alexandrov and others solved the problem in general. However, this last solution does not provide any … cryptococcus morfologiaWebLp-Minkowski problem is quite different from the path taken in [Lul] in solving the even Lp-Minkowski problem. The solution to the volume-normalized even Lp-Minkowski problem for all p > 1 is needed in [LuYZ2]. A compact convex subset of Euclidean n-space Rn will be called a convex body. Associated with a convex body K is its support function h ... durham academy tuition costWebThe Minkowski Problem concerns the existence, uniqueness, and regularity of closed convex hypersurfaces whose Gauss curvature (as a function of the outer normals) is … durham accounting and finance courseWebThe works of Guan and Lin [8] and Chou and Wang [5] focus on existence and regularity for the L p Minkowski problem. Both works make use of the machinery of the theory of … cryptococcus ncbiWebA volume-normalized formulation of the L p-Minkowski problem is presented. This formulation has the advantage that a solution is possible for all p ≥ 1, including the … durham academy staff directory