منابع مشابه
On supporting hyperplanes to convex bodies∗
Given a convex set and an interior point close to the boundary, we prove the existence of a supporting hyperplane whose distance to the point is controlled, in a dimensionally quantified way, by the thickness of the convex set in the orthogonal direction. This result has important applications in the regularity theory for Monge-Ampère type equations arising in optimal transportation.
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The notion of even valuation is introduced as a natural generalization of volume on compact convex subsets of Euclidean space. A recent characterization theorem for volume leads in turn to a connection between even valuations on compact convex sets and continuous functions on Grassmannians. This connection can be described in part using generating distributions for symmetric compact convex sets...
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Consider the set B = [0, 1] endowed with the operations⊕ = max,∧ = min. This is a well-known distributive lattice, and like any distributive lattice it can be considered as a semiring equipped with addition ⊕ and multiplication ⊗ := ∧. Importantly, both operations are idempotent, a⊕a = a and a⊗a = a∧a = a, and closely related to the order: a⊕ b = b ⇔ a ≤ b ⇔ a∧ b = a. For standard literature on...
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In this paper we introduce a quotient class of pairs of convex bodies in which every member have convex union. The space of pairs of convex bodies has been investigated in a number of papers [3], [8], [9], and [12]. This space has found an application in quasidifferential calculus (cf. [1], [5], [7], [10]). A quasidifferential is represented as a pair of convex bodies and it is essential to fin...
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ژورنال
عنوان ژورنال: Methods and Applications of Analysis
سال: 2013
ISSN: 1073-2772,1945-0001
DOI: 10.4310/maa.2013.v20.n3.a3