A Nijenhuis-type tensor on the quotient of a distribution
A nilpotent Lie algebra and eigenvalue estimates
The aim of this paper is to demonstrate how a fairly simple nilpotent Lie algebra can be used as a tool to study differential operators on with polynomial coefficients, especially when the property studied depends only on the degree of the polynomials involved and/or the number of variables.
A noncommutative 2-sphere generated by the quantum complex plane
S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to q-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a q-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the q-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions...
A nonexistence result for Yamabe type problems on thin annuli
A Non-Existence Theorem for Pluriharmonic Maps of Finite Energy.
A nonlinear parabolic problem on a Riemannian manifold without boundary arising in climatology.
We present some results on the mathematical treatment of a global two-dimensional diffusive climate model. The model is based on a long time averaged energy balance and leads to a nonlinear parabolic equation for the averaged surface temperature. The spatial domain is a compact two-dimensional Riemannian manifold without boundary simulating the Earth. We prove the existence of bounded weak solutions via a fixed point argument. Although, the uniqueness of solutions may fail, in general, we give a...
A nonlinear periodic system with nonsmooth potential of indefinite sign
In this paper we consider a nonlinear periodic system driven by the vector ordinary -Laplacian and having a nonsmooth locally Lipschitz potential, which is positively homogeneous. Using a variational approach which exploits the homogeneity of the potential, we establish the existence of a nonconstant solution.
A nonlinear Poisson transform for Einstein metrics on product spaces
We consider the Einstein deformations of the reducible rank two symmetric spaces of noncompact type. If is the product of any two real, complex, quaternionic or octonionic hyperbolic spaces, we prove that the family of nearby Einstein metrics is parametrized by certain new geometric structures on the Furstenberg boundary of .
A nonlinear second order problem with a nonlocal boundary condition.
A non-linear version of Swan's theorem.
A nonsmooth exponential
Let ℳ be a type II₁ von Neumann algebra, τ a trace in ℳ, and L²(ℳ,τ) the GNS Hilbert space of τ. If L²(ℳ,τ)₊ is the completion of the set of selfadjoint elements, then each element ξ ∈ L²(ℳ,τ)₊ gives rise to a selfadjoint unbounded operator on L²(ℳ,τ). In this note we show that the exponential exp: L²(ℳ,τ)₊ → L²(ℳ,τ), , is continuous but not differentiable. The same holds for the Cayley transform . We also show that the unitary group with the strong operator topology is not an embedded submanifold...
A note on Banach spaces and sub differentials of convex functions
A note on Bochner type theorems for complete manifolds.
A Note on Coercivity of Lower Semicontinuous Functions and Nonsmooth Critical Point Theory
The first motivation for this note is to obtain a general version of the following result: let E be a Banach space and f : E → R be a differentiable function, bounded below and satisfying the Palais-Smale condition; then, f is coercive, i.e., f(x) goes to infinity as ||x|| goes to infinity. In recent years, many variants and extensions of this result appeared, see [3], [5], [6], [9], [14], [18], [19] and the references therein. A general result of this type was given in [3, Theorem 5.1] for a lower...
A Note on Differentiability of Lipschitz Maps
We show that every Lipschitz map defined on an open subset of the Banach space C(K), where K is a scattered compactum, with values in a Banach space with the Radon-Nikodym property, has a point of Fréchet differentiability. This is a strengthening of the result of Lindenstrauss and Preiss who proved that for countable compacta. As a consequence of the above and a result of Arvanitakis we prove that Lipschitz functions on certain function spaces are Gâteaux differentiable.
A note on Dirac operators on the quantum punctured disk.
A note on flat noncommutative connections
It is proven that every flat connection or covariant derivative ∇ on a left A-module M (with respect to the universal differential calculus) induces a right A-module structure on M so that ∇ is a bimodule connection on M or M is a flat differentiable bimodule. Similarly a flat hom-connection on a right A-module M induces a compatible left A-action.
A note on geometric characterization of Fréchet differentiability
A note on global Nash subvarieties and Artin-Mazur theorem
It is shown that every connected global Nash subvariety of is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.
A note on harmonic maps between surfaces