Proof of Theorem

In the paper "Liouville-type theorems for a quasilinear elliptic equation of the H´enon-type", We consider the H´enon-type quasilinear elliptic equation −Δmu = |x| aup where Δmu = div(|∇u| m−2∇u), m > 1, p>m − 1 and a ≥ 0. We are concerned with the Liouville property, i.e. the nonexistence of positive solutions in the whole space RN . We prove the optimal Liouville-type theorem for dimension N

13p runordie3 27-06-2022 9 4   Download

We construct an exhaustive submeasure that is not equivalent to a measure. This solves problems of J. von Neumann (1937) and D. Maharam (1947). Contents 1. Introduction 2. Roberts 3. Farah 4. The construction 5. The main estimate 6. Exhaustivity 7. Proof of Theorems 1.2 to 1.4 References 1. Introduction Consider a Boolean algebra B of sets.

30p dontetvui 17-01-2013 82 12   Download

The goal of this paper is to describe all closed, aspherical Riemannian manifolds M whose universal covers M have a nontrivial amount of symmetry. By this we mean that Isom(M ) is not discrete. By the well-known theorem of Myers-Steenrod [MS], this condition is equivalent to [Isom(M ) : π1 (M )] = ∞. Also note that if any cover of M has a nondiscrete isometry group, then so does its universal cover M . Our description of such M is given in Theorem 1.2 below. The proof of this theorem uses methods from Lie theory, harmonic maps,...

27p dontetvui 17-01-2013 58 8   Download

It is well known that not every orientation-preserving homeomorphism of the circle to itself is a conformal welding, but in this paper we prove several results which state that every homeomorphism is “almost” a welding in a precise way. The proofs are based on Koebe’s circle domain theorem. We also give a new proof of the well known fact that quasisymmetric maps are conformal weldings. 1. Introduction Let D ⊂ R2 be the open unit disk, let D∗ = S 2 \D and let T = ∂D = ∂D∗ be the unit circle. ...

45p dontetvui 17-01-2013 52 9   Download

We prove analogues for hypergraphs of Szemer´di’s regularity lemma and e the associated counting lemma for graphs. As an application, we give the first combinatorial proof of the multidimensional Szemer´di theorem of Furstenberg e and Katznelson, and the first proof that provides an explicit bound. Similar results with the same consequences have been obtained independently by Nagle, R¨dl, Schacht and Skokan. o 1.

51p noel_noel 17-01-2013 70 8   Download

Let k be a local field, and Γ ≤ GLn (k) a linear group over k. We prove that Γ contains either a relatively open solvable subgroup or a relatively dense free subgroup. This result has applications in dynamics, Riemannian foliations and profinite groups. Contents 1. Introduction 2. A generalization of a lemma of Tits 3. Contracting projective transformations 4. Irreducible representations of non-Zariski connected algebraic groups 5. Proof of Theorem 1.3 in the finitely generated case 6. Dense free subgroups with infinitely many generators 7.

49p noel_noel 17-01-2013 62 8   Download

Let X = G/H be a reductive symmetric space and K a maximal compact subgroup of G. The image under the Fourier transform of the space of K-finite compactly supported smooth functions on X is characterized. Contents 1. Introduction 2. Notation 3. The Paley-Wiener space. Main theorem 4. Pseudo wave packets 5. Generalized Eisenstein integrals 6. Induction of Arthur-Campoli relations 7. A property of the Arthur-Campoli relations 8. Proof of Theorem 4.4 9.

32p noel_noel 17-01-2013 34 6   Download

We describe a Schubert induction theorem, a tool for analyzing intersections on a Grassmannian over an arbitrary base ring. The key ingredient in the proof is the Geometric Littlewood-Richardson rule of [V2]. As applications, we show that all Schubert problems for all Grassmannians are enumerative over the real numbers, and sufficiently large finite fields. We prove a generic smoothness theorem as a substitute for the Kleiman-Bertini theorem in positive characteristic.

25p noel_noel 17-01-2013 55 6   Download

Annals of Mathematics This is the first in a series of papers whereby we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we give new improved bounds for linear forms in three logarithms. We also apply a combination of classical techniques with the modular approach to show that the only perfect powers in the Fibonacci sequence are 0, 1, 8 and 144 and the only perfect powers in the Lucas sequence are 1...

51p noel_noel 17-01-2013 49 8   Download

This paper gives a quantitative version of Thurston’s hyperbolic Dehn surgery theorem. Applications include the first universal bounds on the number of nonhyperbolic Dehn fillings on a cusped hyperbolic 3-manifold, and estimates on the changes in volume and core geodesic length during hyperbolic Dehn filling. The proofs involve the construction of a family of hyperbolic conemanifold structures, using infinitesimal harmonic deformations and analysis of geometric limits.

56p noel_noel 17-01-2013 59 6   Download

This paper is devoted to the proof of the orbifold theorem: If O is a compact connected orientable irreducible and topologically atoroidal 3-orbifold with nonempty ramification locus, then O is geometric (i.e. has a metric of constant curvature or is Seifert fibred). As a corollary, any smooth orientationpreserving nonfree finite group action on S 3 is conjugate to an orthogonal action. Contents 1. Introduction 2. 3-dimensional orbifolds 2.1. Basic definitions 2.2. Spherical and toric decompositions 2.3. Finite group actions on spheres with fixed points 2.4.

97p noel_noel 17-01-2013 53 7   Download

We show that any set containing a positive proportion of the primes contains a 3-term arithmetic progression. An important ingredient is a proof that the primes enjoy the so-called Hardy-Littlewood majorant property. We derive this by giving a new proof of a rather more general result of Bourgain which, because of a close analogy with a classical argument of Tomas and Stein from Euclidean harmonic analysis, might be called a restriction theorem for the primes. 1. Introduction Arguably the second most famous result of Klaus Roth is his 1953 upper bound [21] on r3 (N ), defined 17 years...

29p noel_noel 17-01-2013 59 7   Download

We study the L2 -convergence of two types of ergodic averages. The first is the average of a product of functions evaluated at return times along arithmetic progressions, such as the expressions appearing in Furstenberg’s proof of Szemer´di’s theorem.

93p noel_noel 17-01-2013 60 6   Download

We study the integral points on surfaces by means of a new method, relying on the Schmidt Subspace Theorem. This method was recently introduced in [CZ] for the case of curves, leading to a new proof of Siegel’s celebrated theorem that any affine algebraic curve defined over a number field has only finitely many S-integral points, unless it has genus zero and not more than two points at infinity. Here, under certain conditions involving the intersection matrix of the divisors at infinity, we shall conclude that the integral points on a surface all lie on a curve. We shall...

23p tuanloccuoi 04-01-2013 59 7   Download

We prove Maruyama’s conjecture on the boundedness of slope semistable sheaves on a projective variety defined over a noetherian ring. Our approach also gives a new proof of the boundedness for varieties defined over a characteristic zero field. This result implies that in mixed characteristic the moduli spaces of Gieseker semistable sheaves are projective schemes of finite type. The proof uses a new inequality bounding slopes of the restriction of a sheaf to a hypersurface in terms of its slope and the discriminant.

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The induction hypotheses Application to endoscopic and stable expansions Cancellation of p-adic singularities Separation by infinitesimal character Elimination of restrictions on f Local trace formulas Local Theorem 1 Weak approximation Global Theorems 1 and 2 10. Concluding remarks Introduction This paper is the last of three articles designed to stabilize the trace formula. Our goal is to stabilize the global trace formula for a general connected group, subject to a condition on the fundamental lemma that has been established in some special cases.

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This paper introduces a rigorous computer-assisted procedure for analyzing hyperbolic 3-manifolds. This procedure is used to complete the proof of several long-standing rigidity conjectures in 3-manifold theory as well as to provide a new lower bound for the volume of a closed orientable hyperbolic 3-manifold. Theorem 0.1. Let N be a closed hyperbolic 3-manifold.

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EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR A CLASS OF DEGENERATE NONLINEAR ELLIPTIC EQUATIONS ˘ MIHAI MIHAILESCU Received 11 January 2005; Revised 4 July 2005; Accepted 17 July 2005 The goal of this paper is to study the existence and the multiplicity of non-trivial weak solutions for some degenerate nonlinear elliptic equations on the whole space RN . The solutions will be obtained in a subspace of the Sobolev space W 1,p (RN ). The proofs rely essentially on the Mountain Pass theorem and on Ekeland’s Variational principle. Copyright © 2006 Mihai Mih˘ ilescu.

17p sting12 10-03-2012 57 4   Download

OF INVARIANT FIBER BUNDLES FOR DYNAMIC EQUATIONS ON MEASURE CHAINS ¨ CHRISTIAN POTZSCHE AND STEFAN SIEGMUND Received 8 August 2003 m -SMOOTHNESS We present a new self-contained and rigorous proof of the smoothness of invariant fiber bundles for dynamic equations on measure chains or time scales. Here, an invariant fiber bundle is the generalization of an invariant manifold to the nonautonomous case.

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Tuyển tập các báo cáo nghiên cứu khoa học ngành toán học tạp chí Department of Mathematic dành cho các bạn yêu thích môn toán học đề tài: Hybrid Proofs of the q-Binomial Theorem and other identities...

21p thulanh7 05-10-2011 52 3   Download