Related papers: Lp bilinear quasimode estimates

Let M be a compact manifold of dimension n, P = P(h) a semiclassical pseudodifferential operator on M, and u = u(h) an L^2 normalised family of functions such that Pu is O(h) in L^2(M) as h goes to 0. Let H be a compact submanifold of M. In…

We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a $TT^*$ argument, simply by using the $L^2$-boundedness of the Hilbert transform on $\R$, we…

We study the sharp $\mathrm{L}^\infty$ estimates for fully non-linear elliptic equations on compact complex manifolds. For the case of K\"ahler manifolds, we prove that the oscillation of any admissible solution to a degenerate fully…

We give a short proof of the duality theorem for the reduced $L_p$-cohomology of a complete oriented Riemannian manifold.

In this paper, we investigate critical quasilinear elliptic partial differential equations on a complete Riemannian manifold with nonnegative Ricci curvature. By exploiting a new and sharp nonlinear Kato inequality and establishing some…

We develop a theory of multidimensional randomization in Lebesgue spaces $L^p$ with the aid of Kahane-Khintchine-Marcus-Pisier inequalities. More precisely, we obtain a result in the spirit of Maurey-Pisier's theorem which involves random…

The paper focuses on the $L^{p}$-Positivity Preservation property ($L^{p}$-PP for short) on a Riemannian manifold $(M,g)$. It states that any $L^p$ function $u$ with $1<p<+\infty$, which solves $(-\Delta + 1)u\ge 0$ on $M$ in the sense of…

We show that the upper bounds for the $L^2$-norms of $L^1$-normalized quasimodes that we obtained in [9] are always sharp on any compact space form. This allows us to characterize compact manifolds of constant sectional curvature using the…

We derive a priori estimates for solutions of a general class of fully non-linear equations on compact Hermitian manifolds. Our method is based on ideas that have been used for different specific equations, such as the complex…

We obtain sharp estimates involving the mean curvatures of higher order of a complete bounded hypersurface immersed in a complete Riemannian manifold. Similar results are also given for complete spacelike hypersurfaces in Lorentzian ambient…

In this paper, we prove a finite dimensional approximation scheme for the Wiener measure on closed Riemannian manifolds, establishing a generalization for $L^{1}$-functionals, of the approach followed by Andersson and Driver on [1]. We…

We show that all the common definitions of quasiregular mappings $f\colon M\to N$ between two equiregular subRiemannian manifolds of homogeneous dimension $Q\geq 2$ are quantitatively equivalent with precise dependences of the…

We prove $L^p\to L^{p'}$ bounds for the resolvent of the Laplace-Beltrami operator on a compact Riemannian manifold of dimension $n$ in the endpoint case $p=2(n+1)/(n+3)$. It has the same behavior with respect to the spectral parameter $z$…

We establish plurisubharmonicity of the envelope of Lelong functional on almost complex manifolds of real dimension four, thereby we generalize the corresponding result for complex manifolds.

We provide a general scheme for proving $L^p$ estimates for certain bilinear Fourier restrictions outside the locally $L^2$ setting. As an application, we show how such estimates follow for the lacunary polygon. In contrast with prior…

In this paper, we address several interconnected problems in the theory of harmonic maps between Riemannian manifolds. First, we present necessary background and establish one of the main results of the paper: a criterion characterizing…

We prove quenched~$L^p$--type estimates for the gradient of a solution of a quasilinear elliptic equation with random coefficients.

Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying $\mathrm{Ric}_{\infty} \ge 1$, we give an $L^1$-estimate exhibiting that the push-forward of the reference measure by the guiding function (arising from the…

The space of all non degenerate bilinear structures on a manifold $M$ carries a one parameter family of pseudo Riemannian metrics. We determine the geodesic equation, covariant derivative, curvature, and we solve the geodesic equation…

An explicit Bellman function is used to prove a bilinear embedding theorem for operators associated with general multi-dimensional orthogonal expansions on product spaces. This is then applied to obtain $L^p,$ $1<p<\infty,$ boundedness of…