Note on the second variation in an isoperimetric problem
نویسندگان
چکیده
منابع مشابه
Remarks on an Edge Isoperimetric Problem
Among all collections of a given number of k-element subsets of an n-element groundset find a collection which maximizes the number of pairs of subsets which intersect in k − 1 elements. This problem was solved for k = 2 by Ahlswede and Katona, and is open for k > 2. We survey some linear algebra approaches which yield to estimations for the maximum number of pairs, and we present a new and sho...
متن کاملA Note on the Global Minimizers of the Nonlocal Isoperimetric Problem in Two Dimensions
In this article we analyze the minimization of the so-called nonlocal isoperimetric problem (NLIP) posed on the flat 2-torus. After establishing regularity of the free boundary of minimizers, we show that when the parameter controlling the influence of the nonlocality is small, there is an interval of values for the mass constraint such that the global minimizer is exactly lamellar; that is, th...
متن کاملThe Isoperimetric Problem
formulation is useful in some areas such as discrete geometry, probability and Banach space theory; see for instance [36] and [49]. The Isoperimetric profile Iμ = I(ds2,μ) of (M, μ) is defined, as above, by Iμ(t) = inf {μ + (R) : μ(R) = t}, 0 ≤ t ≤ μ(M). If we change the metric or the measure by a positive factor a, it follows easily that Iaμ(t) = aIμ( t a ) and I(a2ds2,μ) = 1 a I(ds2,μ). Among...
متن کاملThe Periodic Isoperimetric Problem
Given a discrete group G of isometries of R3, we study the Gisoperimetric problem, which consists of minimizing area (modulo G) among surfaces in R3 which enclose a G-invariant region with a prescribed volume fraction. If G is a line group, we prove that solutions are either families of round spheres or right cylinders. In the doubly periodic case we prove that for most rank two lattices, solut...
متن کاملThe Vertex Isoperimetric Problem on Kneser Graphs
For a simple graph G = (V,E), the vertex boundary of a subset A ⊆ V consists of all vertices not in A that are adjacent to some vertex in A. The goal of the vertex isoperimetric problem is to determine the minimum boundary size of all vertex subsets of a given size. In particular, define μG(r) as the minimum boundary size of all vertex subsets of G of size r. Meanwhile, the vertex set of the Kn...
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: Bulletin of the American Mathematical Society
سال: 1908
ISSN: 0002-9904
DOI: 10.1090/s0002-9904-1908-01630-6