A smooth map f: M ! N between semi-riemannian manifolds is called a harmonic morphism if f pulls back harmonic functions (i.e., local solutions of the Laplace{Beltrami equation) on N into harmonic functions on M. It is shown that a harmonic morphism is the same as a harmonic map which is moreover horizontally weakly conformal, these two notions being likewise carried over from the riemannian ca...

we classify the paracontact riemannian manifolds that their rieman-nian curvature satisfies in the certain condition and we show that thisclassification is hold for the special cases semi-symmetric and locally sym-metric spaces. finally we study paracontact riemannian manifolds satis-fying r(x, ξ).s = 0, where s is the ricci tensor.

The Laplace-Beltrami operator of a smooth Riemannian manifold is determined by the Riemannian metric. Conversely, the heat kernel constructed from its eigenvalues and eigenfunctions determines the Riemannian metric. This work proves the analogy on Euclidean polyhedral surfaces (triangle meshes), that the discrete Laplace-Beltrami operator and the discrete Riemannian metric (unique up to a scali...

Our goal is to study quantities in Riemannian geometry which remain invariant under the “conformal change of metrics”–that is, under changes of metrics which stretch the length of vectors but preserve the angles between any pair of vectors. We call such a quantity “conformally invariant”. In conjunction with the study of conformal invariants, we are also interested in studying “conformally cova...

Motivated by Nash equilibrium problems on ’curved’ strategy sets, the concept of Nash-Stampacchia equilibrium points is introduced for a finite family of non-smooth functions defined on geodesic convex sets of certain Riemannian manifolds. Characterization, existence, and stability of NashStampacchia equilibria are studied when the strategy sets are compact/noncompact subsets of certain Hadamar...

We show that, under some very weak assumption of effective variation for the magnetic field, a periodic Schrödinger operator with magnetic wells on a noncompact Riemannian manifold M such that H(M, R) = 0 equipped with a properly disconnected, cocompact action of a finitely generated, discrete group of isometries has an arbitrarily large number of spectral gaps in the semi-classical limit.

‎let $x,y$ be normed spaces with $l(x,y)$ the space of continuous‎ ‎linear operators from $x$ into $y$‎. ‎if ${t_{j}}$ is a sequence in $l(x,y)$,‎ ‎the (bounded) multiplier space for the series $sum t_{j}$ is defined to be‎ [ ‎m^{infty}(sum t_{j})={{x_{j}}in l^{infty}(x):sum_{j=1}^{infty}%‎ ‎t_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $s:m^{infty}(sum t_{j})rightarrow y$ associat...

we establish a sharp maximal function estimate for some vector-valued multilinear singular integral operators. as an application, we obtain the $(l^p, l^q)$-norm inequality for vector-valued multilinear operators.

A notion of quasi-regularity is extended for the inclusion problem F(p) ∈ C , where F is a differentiable mapping from a Riemannian manifold M to Rn . When C is the set of minimum points of a convex real-valued function h on Rn and DF satisfies the L-average Lipschitz condition, we use the majorizing function technique to establish the semi-local convergence of sequences generated by the Gauss-...