ﻻ يوجد ملخص باللغة العربية
Let $(X,g)$ be a compact manifold with conic singularities. Taking $Delta_g$ to be the Friedrichs extension of the Laplace-Beltrami operator, we examine the singularities of the trace of the half-wave group $e^{- i t sqrt{ smash[b]{Delta_g}}}$ arising from strictly diffractive closed geodesics. Under a generic nonconjugacy assumption, we compute the principal amplitude of these singularities in terms of invariants associated to the geodesic and data from the cone point. This generalizes the classical theorem of Duistermaat-Guillemin on smooth manifolds and a theorem of Hillairet on flat surfaces with cone points.
We revisit the paper [Mel86] by R. Melrose, providing a full proof of the main theorem on propagation of singularities for subelliptic wave equations, and linking this result with sub-Riemannian geometry. This result asserts that singularities of sub
We consider manifolds with conic singularites that are isometric to $mathbb{R}^{n}$ outside a compact set. Under natural geometric assumptions on the cone points, we prove the existence of a logarithmic resonance-free region for the cut-off resolvent
We provide sufficient conditions under which the difference of the resolvents of two higher-order operators acting in $R^N$ belongs to trace classes $cC^p$. We provide explicit estimates on the norm of the resolvent difference in terms of $L^p$ norms
A conic bundle is a contraction $Xto Z$ between normal varieties of relative dimension $1$ such that $-K_X$ is relatively ample. We prove a conjecture of Shokurov which predicts that, if $Xto Z$ is a conic bundle such that $X$ has canonical singulari
We consider a family of spherically symmetric, asymptotically Euclidean manifolds with two trapped sets, one which is unstable and one which is semi-stable. The phase space structure is that of an inflection transmission set. We prove a sharp local s