منابع مشابه
On De Giorgi Conjecture in Dimension
A celebrated conjecture due to De Giorgi states that any bounded solution of the equation ∆u+(1−u2)u = 0 in RN with ∂yN u > 0 must be such that its level sets {u = λ} are all hyperplanes, at least for dimension N ≤ 8. A counterexample for N ≥ 9 has long been believed to exist. Based on a minimal graph Γ which is not a hyperplane, found by Bombieri, De Giorgi and Giusti in RN , N ≥ 9, we prove t...
متن کاملOn De Giorgi’s Conjecture in Dimension
A celebrated conjecture due to De Giorgi states that any bounded solution of the equation ∆u+(1−u2)u = 0 in RN with ∂yN u > 0 must be such that its level sets {u = λ} are all hyperplanes, at least for dimension N ≤ 8. A counterexample for N ≥ 9 has long been believed to exist. Starting from a minimal graph Γ which is not a hyperplane, found by Bombieri, De Giorgi and Giusti in RN , N ≥ 9, we pr...
متن کاملOn De Giorgi Conjecture in Dimension N ≥ 9
A celebrated conjecture due to De Giorgi states that any bounded solution of the equation ∆u+(1−u2)u = 0 in RN with ∂yN u > 0 must be such that its level sets {u = λ} are all hyperplanes, at least for dimension N ≤ 8. A counterexample for N ≥ 9 has long been believed to exist. Based on a minimal graph Γ which is not a hyperplane, found by Bombieri, De Giorgi and Giusti in RN , N ≥ 9, we prove t...
متن کاملOn Keller's Conjecture in Dimension Seven
A cube tiling of R is a family of pairwise disjoint cubes [0, 1) + T = {[0, 1) + t : t ∈ T} such that ⋃ t∈T ([0, 1) d + t) = R. Two cubes [0, 1) + t, [0, 1) + s are called a twin pair if |tj − sj | = 1 for some j ∈ [d] = {1, . . . , d} and ti = si for every i ∈ [d] \ {j}. In 1930, Keller conjectured that in every cube tiling of R there is a twin pair. Keller’s conjecture is true for dimensions ...
متن کاملA short proof of the maximum conjecture in CR dimension one
In this paper and by means of the extant results in the Tanaka theory, we present a very short proof in the specific case of CR dimension one for Beloshapka's maximum conjecture. Accordingly, we prove that each totally nondegenerate model of CR dimension one and length >= 3 has rigidity. As a result, we observe that the group of CR automorphisms associated with each of such models contains onl...
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ژورنال
عنوان ژورنال: Annals of Mathematics
سال: 2011
ISSN: 0003-486X
DOI: 10.4007/annals.2011.174.3.3