Related papers: Semi-classical calculus on manifolds with ends and…
Compact pseudo-Riemannian manifolds that have parallel Weyl tensor without being conformally flat or locally symmetric are known to exist in infinitely many dimensions greater than 4. We prove some general topological properties of such…
We give a sufficient condition to rule out complete Riemannian metrics with nonnegative scalar curvature on the interiors of handlebodies. In higher dimensions, we give examples of ends of manifolds with positive scalar curvature metrics.
In this article, we shall construct the resolvent of Laplacian at high energies near the spectrum on non-product conic manifolds with a single cone tip. Microlocally, the resolvent kernel is the sum of b-pseudodifferential operators,…
We derive estimates relating the values of a solution at any two points to the distance between the points, for quasilinear isotropic elliptic equations on compact Riemannian manifolds, depending only on dimension and a lower bound for the…
We develop potential theory for $m$-subharmonic functions with respect to a Hermitian metric on a Hermitian manifold. First, we show that the complex Hessian operator is well-defined for bounded functions in this class. This allows to…
Expository paper on the relations between perturbation theory of pseudo-differential operators, finiteness theorems and deformations of Lagrangian varieties.
We consider a class of fully non-linear parabolic equations on compact Hermitian manifolds involving symmetric functions of partial Laplacians. Under fairly general assumptions, we show the long time existence and convergence of solutions.…
In this paper we obtain a complete characterization of pseudo-collarable $n$-manifolds for $n\geq 6$. This extends earlier work by Guilbault and Tinsley to allow for manifolds with noncompact boundary. In the same way that their work can be…
In this article, we investigate the unweighted and weighted $L^p$-boundedness of pseudo-multipliers associated with a class of Schr\"odinger operators. The weight classes we consider are tailored to this framework and strictly contain the…
We give a simple construction of new, complete, finite volume manifolds $M$ of bounded, nonpositive curvature. These manifolds have ends that look like a mixture of locally symmetric ends of different ranks and their fundamental groups are…
We prove $R$-bisectoriality and boundedness of the $H^\infty$-functional calculus in $L^p$ for all $1<p<\infty$ for the Hodge-Dirac operator associated with Witten Laplacians on complete Riemannian manifolds with non-negative Bakry-Emery…
A review is made of the basic tools used in mathematics to define a calculus for pseudodifferential operators on Riemannian manifolds endowed with a connection: esistence theorem for the function that generalizes the phase; analogue of…
In this paper we provide an integral representation of the fractional Laplace-Beltrami operator for general riemannian manifolds which has several interesting applications. We give two different proofs, in two different scenarios, of…
This paper contains a set of lecture notes on manifolds with boundary and corners, with particular attention to the space of quantum states. A geometrically inspired way of dealing with these kind of manifolds is presented,and explicit…
We establish the existence of multiple solutions for a nonvariational elliptic systems involving $p(x)$-Laplacian operator. The approach combines the methods of sub-supersolution and Leray--Schauder topological degree.
We give some properties of semi-symmetric pseudo-Riemannian manifolds. These are foliated manifolds and for the Lorentzian metric, the Ricci operator has only real eigenvalues.
The main scalar-mean extremality and rigidity results in the existing literature concern manifolds whose curvature operators are nonnegative, or warped product spaces with a log-concave warping function whose leaves carry metrics of…
We introduce different classical characteristics used to regularize a subharmonic function and compare them. As an application we give a complete proof of a useful characterization of the modulus of continuity of such functions in terms of…
The paper is devoted to Hardy type inequalities on closed manifolds. By means of various weighted Ricci curvatures, we establish several sharp Hardy type inequalities on closed weighted Riemannian manifolds. Our results complement in…
In the present paper we study some kinds of the problems for the bi-drifting Laplacian operator and get some sharp lower bounds for the first eigenvalue for these eigenvalue problems on compact manifolds with boundary (also called a smooth…