Related papers: Sharp uncertainty principles on general Finsler ma…

In this paper, we prove two rigidity results for non-positively curved homogeneous Finsler metrics. Our first main result yields an extension of Hu-Deng's well-known result proven for the Randers metrics. Indeed, we prove that every…

One of the formulations of Heisenberg uncertainty principle, concerning so-called measurement uncertainty, states that the measurement of one observable modifies the statistics of the other. Here, we derive such a measurement uncertainty…

We analyze the foundations of Finsler gravity theories with metric compatible connections constructed on nonholonomic tangent bundles, or (pseudo) Riemannian manifolds. There are considered "minimal" modifications of Einstein gravity…

In this article, we establish the $L^p$-Heisenberg-Pauli-Weyl uncertainty inequalities on the Laguerre hypergroup $\mathbb{K}$, the natural setting for radial analysis on the Heisenberg group. For $1 \leq p < 2$, under the condition $b >…

For metric measure spaces verifying the reduced curvature-dimension condition $CD^*(K,N)$ we prove a series of sharp functional inequalities under the additional assumption of essentially non-branching. Examples of spaces entering this…

The entropic way of formulating Heisenberg's uncertainty principle not only plays a fundamental role in applications of quantum information theory but also is essential for manifesting genuine nonclassical features of quantum systems. In…

We find sharp bounds for the norm inequality on a Pseudo-hermitian manifold, where the L^2 norm of all second derivatives of the function involving horizontal derivatives is controlled by the L^2 norm of the sub-Laplacian. Perturbation…

We study a special class of Finsler metrics which we refer to as Almost Rational Finsler metrics (shortly, AR-Finsler metrics). We give necessary and sufficient conditions for an AR-Finsler manifold $(M,F)$ to be Riemannian. The rationality…

We are interested in the Caffarelli-Kohn-Nirenberg inequality (CKN in short), introduced by these authors in 1984. We explain why the CKN inequality can be viewed as a Sobolev inequality on a weighted Riemannian manifold. More precisely, we…

Heisenberg's uncertainty principle, exemplified by the gamma ray thought experiment, suggests that any finite precision measurement disturbs any observables noncommuting with the measured observable. Here, it is shown that this statement…

We establish optimal stability estimates in terms of the Fraenkel asymmetry with universal dimensional constants for a Lorentzian isoperimetric inequality due to Bahn and Ehrlich and, as a consequence, for a special version of a Lorentzian…

We prove sharp inequalities for determinants of Toeplitz operators and twisted Laplace operators on the two-sphere, generalizing the Moser-Trudinger-Onofri inequality. In particular a sharp version of conjectures of Gillet-Soule and Fang…

Heisenberg's uncertainty principle was originally posed for the limit of the accuracy of simultaneous measurement of non-commuting observables as stating that canonically conjugate observables can be measured simultaneously only with the…

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…

We prove quantitative stability of isometries on the first Heisenberg group with sub-Riemannian geometry: every $ (1+ \varepsilon)$-quasi-isometry of the John domain of the Heisenberg group $ \mathbb {H} $ is close to some isometry with…

In this paper, we study weakly orthogonally invariant Finsler metrics and derive explicit expressions for their Berwald and Landsberg curvatures. We then obtain the system of partial differential equations characterizing generalized Finsler…

For every Finsler metric $F$ we associate a Riemannian metric $g_F$ (called the Binet-Legendre metric). The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previous constructions. The…

We prove the Heisenberg-Pauli-Weyl inequality, Hardy-Sobolev inequality, and Caffarelli-Kohn-Nirenberg (CKN) inequality on manifolds with nonnegative Ricci curvature and Euclidean volume growth, of dimension n>=3.

In this paper, a class of holomorphic invariant metrics is introduced on the irreducible classical domains of type I-IV, which are strongly pseudoconvex complex Finsler metrics in the strict sense of M. Abate and G. Patrizio[2]. These…

The aim of the paper is two-fold. First, we provide an explicit form of the functions for which equality holds for the uncertainty inequalities studied in \cite{Fei}. Second, we establish an $L^p$-type Heisenberg-Pauli-Weyl uncertainty…