Results 61 to 70 of about 33,123 (219)

Global and microlocal aspects of Dirac operators: Propagators and Hadamard states

Mathematische Nachrichten, EarlyView.
Abstract We propose a geometric approach to construct the Cauchy evolution operator for the Lorentzian Dirac operator on Cauchy‐compact globally hyperbolic 4‐manifolds. We realize the Cauchy evolution operator as the sum of two invariantly defined oscillatory integrals—the positive and negative Dirac propagators—global in space and in time, with ...
Matteo Capoferri, Simone Murro
wiley   +1 more source

On the Alexandrov Topology of sub-Lorentzian Manifolds

, 2013
It is commonly known that in Riemannian and sub-Riemannian Geometry, the metric tensor on a manifold defines a distance function. In Lorentzian Geometry, instead of a distance function it provides causal relations and the Lorentzian time-separation ...
A Korolko, A Korolko, A Korolko, AA Agrachev, B O'Neill, DC Chang, E Grong, JK Beem, L Capogna, M Grochowski, M Grochowski, M Grochowski, PK Rashevski, R Montgomery, R Montgomery, RS Strichartz, SW Hawking, W Liu, WL Chow   +18 more
core   +1 more source

Initial State Privacy of Nonlinear Systems on Riemannian Manifolds

International Journal of Robust and Nonlinear Control, EarlyView.
ABSTRACT In this paper, we investigate initial state privacy protection for discrete‐time nonlinear closed systems. By capturing Riemannian geometric structures inherent in such privacy challenges, we refine the concept of differential privacy through the introduction of an initial state adjacency set based on Riemannian distances.
Le Liu, Yu Kawano, Antai Xie, Ming Cao
wiley   +1 more source

Braided spaces with dilations and sub-riemannian symmetric spaces [PDF]

, 2011
Braided sets which are also spaces with dilations are presented and explored in this paper, in the general frame of emergent algebras arxiv:0907.1520. Examples of such spaces are the sub-riemannian symmetric spaces.
Buliga, Marius
core  

Invariants of contact sub-pseudo-Riemannian structures and Einstein-Weyl geometry

, 2015
We consider local geometry of sub-pseudo-Riemannian structures on contact manifolds. We construct fundamental invariants of the structures and show that the structures give rise to Einstein-Weyl geometries in dimension 3, provided that certain additional
Grochowski, Marek, Krynski, Wojciech
core   +1 more source

Social Rationality and Human Reasoning: Logical Expressivism and the Flat Mind

Topics in Cognitive Science, EarlyView.
Abstract This paper attempts to reconcile the claims that the mind is both flat (Chater, 2018) and highly rational (Oaksford & Chater, 2020). According to the flat mind hypothesis, the mind is a mass of inconsistent and contradictory fragments of experience.
Mike Oaksford
wiley   +1 more source

On an evolution equation in sub-Finsler geometry

Analysis and Geometry in Metric Spaces
We study the gradient flow of an energy with mixed homogeneity, which is at the interface of Finsler and sub-Riemannian geometry.
Garofalo Nicola
doaj   +1 more source

Projection methods for some constrained systems [PDF]

Rendiconti di Matematica e delle Sue Applicazioni, 2003
This article is concerned with a geometric tool given by a pair of projector operators defined by almost product structures on finite dimensional manifolds, polarized by a distribution of constant rank and also endowed with some geometric structures ...
Paulo Pitanga, Paulo R. Rodrigues
doaj  

Removing scalar curvature assumption for Ricci flow smoothing

Bulletin of the London Mathematical Society, EarlyView.
Abstract In recent work of Chan–Huang–Lee, it is shown that if a manifold enjoys uniform bounds on (a) the negative part of the scalar curvature, (b) the local entropy, and (c) volume ratios up to a fixed scale, then there exists a Ricci flow for some definite time with estimates on the solution assuming that the local curvature concentration is small ...
Adam Martens
wiley   +1 more source

Qualitative properties of the heat content

Bulletin of the London Mathematical Society, EarlyView.
Abstract We obtain monotonicity and convexity results for the heat content of domains in Riemannian manifolds and in Euclidean space subject to various initial temperature conditions. We introduce the notion of a strictly decreasing temperature set, and show that it is a sufficient condition to ensure monotone heat content.
Michiel van den Berg, Katie Gittins
wiley   +1 more source