相关论文: An uncertainty principle on compact manifolds

The reduced system in the problem of the inertial motion of a rigid body with a fixed point (the Euler case) is equivalent, by the Maupertuis principle, to some geodesic flow on the 2-sphere. We describe the phase topology of this case…

In this paper, we provide the Heisenberg's inequality and the Hardy's theorem for the Clifford-Fourier transform on $\mathbb{R}^m$.

We study the boundary rigidity problem for compact Riemannian manifolds with boundary $(M,g)$: is the Riemannian metric $g$ uniquely determined, up to an action of diffeomorphism fixing the boundary, by the distance function $\rho_g(x,y)$…

We review some recent results concerning integrable quantum field theories in 1+1 space-time dimensions which contain unstable particles in their spectrum. Recalling first the main features of analytic scattering theories associated to…

We compute the homotopy type of the moduli space of flat, unitary connections over aspherical surfaces, after stabilizing with respect to the rank of the underlying bundle. Over the orientable surface M^g, we show that this space has the…

In this paper, we prove that some renowned lower bounds in discrepancy theory admit a discrete analogue. Namely, we prove that the lower bound of the discrepancy for corners in the unit cube due to Roth holds true also for a suitable finite…

Seiberg-Witten theory leads to a delicate interplay between Riemannian geometry and smooth topology in dimension four. In particular, the scalar curvature of any metric must satisfy certain non-trivial estimates if the manifold in question…

Heisenberg's uncertainty principle is one of the main tenets of quantum theory. Nevertheless, and despite its fundamental importance for our understanding of quantum foundations, there has been some confusion in its interpretation: although…

Let $\mathcal{M}_{0}^n$ be the class of closed, simply-connected, non-negatively curved Riemannian manifolds admitting an isometric, effective, isotropy-maximal torus action. We prove that if $M\in \mathcal{M}_{0}^n$, then $M$ is…

We investigate the structure of the gravity-induced Generalized Uncertainty Principle in three dimensions. The subtleties of lower dimensional gravity, and its important differences with respect to four and higher dimensions, are duly taken…

For closed oriented manifolds, we establish oriented homotopy invariance of higher signatures that come from the fundamental group of a large class of orientable 3-manifolds, including the ``piecewise geometric'' ones in the sense of…

A manifold is a space that locally looks like the smooth space $\mathbf{R}^{n}$. It is usually also assumed that the underlying topological space of a manifold is hausdorff. However, there are natural examples of manifolds for which the…

Let $\mathbb{T}$ be the unit circle and $\Gamma\setminus G$ the 3-dimensional Heisenberg nilmanifold. We prove that the M\"obius function is linearly disjoint from a class of distal skew products on $\mathbb{T}\times\Gamma\setminus G$.…

In this paper, we consider locally wedge-shaped manifolds, which are Riemannian manifolds that are allowed to have both boundary and certain types of edges. We define and study the properties of free boundary minimal hypersurfaces inside…

Recently Kosaki proved an uncertainty principle for matrices, related to Wigner-Yanase-Dyson information, and asked if a similar inequality could be proved in the von Neumann algebra setting. In this paper we prove such an uncertainty…

By works of Schoen-Yau and Gromov-Lawson any Riemannian manifold with nonnegative scalar curvature and diffeomorphic to a torus is isometric to a flat torus. Gromov conjectured subconvergence of tori with respect to a weak Sobolev type…

Given a general complete Riemannian manifold $M$, we introduce the concept of "local Moser-Trudinger inequality on $W^{1,n}(M)$". We show how the validity of the Moser-Trudinger inequality can be extended from a local to a global scale…

In this paper, we introduce the notation of bi-shift of biprojections in subfactor theory to unimodular Kac algebras. We characterize the minimizers of Hirschman-Beckner uncertainty principle and Donoho-Stark uncertainty principle for…

We use wrapped D-brane probes to measure position dependent perturbations of compactification moduli. Due to the backreaction of the D-branes on the local geometry, we suspect that measuring the fluctuations of one modulus to high precision…

In a recent work [2] with Datta, we introduced the mu vector (with respect to a given field) of simplicial complexes and used it to study tightness and lower bounds. In this paper, we modify the definition of mu vectors. With the new…