Results 31 to 40 of about 2,719,579 (161)

On the Zoll deformations of the Kepler problem

Bulletin of the London Mathematical Society, EarlyView.
Abstract A celebrated result of Bertrand states that the only central force potentials on the plane with the property that all bounded orbits are periodic are the Kepler potential and the potential of the harmonic oscillator. In this paper, we complement Bertrand's theorem showing the existence of an infinite‐dimensional space of central force ...
Luca Asselle, Stefano Baranzini
wiley   +1 more source

Mathematical Support to Braneworld Theory

, 2008
The braneworld theory appear with the purpose of solving the problem of the hierarchy of the fundamental interactions. The perspectives of the theory emerge as a new physics, for example, deviation of the law of Newton's gravity. One of the principles of
Boothby W. M., EDMUNDO M. MONTE, Einsenhart L. P., Jacobowitz H., Kobayashi S.   +4 more
core   +1 more source

Action functional as an early warning indicator in the space of probability measures via Schrödinger bridge

Quantitative Biology, Volume 13, Issue 3, September 2025.
Abstract Critical transitions and tipping phenomena between two meta‐stable states in stochastic dynamical systems are a scientific issue. In this work, we expand the methodology of identifying the most probable transition pathway between two meta‐stable states with Onsager–Machlup action functional, to investigate the evolutionary transition dynamics ...
Peng Zhang, Ting Gao, Jin Guo, Jinqiao Duan   +3 more
wiley   +1 more source

Volume form and its applications in Finsler geometry

, 2011
We establish some volume comparison theorems for general volume forms, and they reduce to the same formulas as Riemannian case for extreme volume form (the maximal or minimal volume form) up to a cofactor. By using the extreme volume form, we are able to
B. Wu
semanticscholar   +1 more source

On the isoperimetric Riemannian Penrose inequality

Communications on Pure and Applied Mathematics, Volume 78, Issue 5, Page 1042-1085, May 2025.
Abstract We prove that the Riemannian Penrose inequality holds for asymptotically flat 3‐manifolds with nonnegative scalar curvature and connected horizon boundary, provided the optimal decay assumptions are met, which result in the ADM$\operatorname{ADM}$ mass being a well‐defined geometric invariant.
Luca Benatti, Mattia Fogagnolo, Lorenzo Mazzieri   +2 more
wiley   +1 more source

The noncommutative Lorentzian cylinder as an isospectral deformation

, 2003
We present a new example of a finite-dimensional noncommutative manifold, namely the noncommutative cylinder. It is obtained by isospectral deformation of the canonical triple associated to the Euclidean cylinder. We discuss Connes' character formula for
Brodzki, Connes, Connes, Connes, Connes, Connes, Dubois-Violette, Elliot, Estrada, Gracia-Bondı́a, Green, Kamani, Konechny, Landsman, Langmann, Nest, Parfionov, Ramazan, Rennie, Rieffel, Rieffel, Rieffel, Rieffel, Schweitzer, Seiberg, Strohmaier, Várilly, Várilly, W. D. van Suijlekom   +28 more
core   +1 more source

Minimizability of developable Riemannian foliations [PDF]

Ann. Global Anal. Geom. 38, Issue 2 119 - 133 (2010), 2009
Let (M,F) be a closed manifold with a Riemannian foliation. We show that the secondary characteristic classes of the Molino's commuting sheaf of (M,F) vanish if (M,F) is developable and the fundamental group of M is of polynomial growth. By theorems of \'{A}lvarez L\'{o}pez, our result implies that (M,F) is minimizable under the same conditions.
arxiv   +1 more source

A Geometric Interpretation for the Algebraic Properties of Second‐Order Ordinary Differential Equations

Mathematical Methods in the Applied Sciences, Volume 48, Issue 6, Page 6912-6917, April 2025.
ABSTRACT Nowadays, a substantial portion of investigations concerning the symmetry analysis of differential equations predominantly adhere to a framework comprising the following key procedures: (i) the derivation of symmetries, (ii) the determination of an optimal system, (iii) the utilization of these symmetries to construct invariants or ...
A. Paliathanasis, S. Moyo, P. G. L. Leach   +2 more
wiley   +1 more source

On some sub-Riemannian objects in hypersurfaces of sub-Riemannian manifolds [PDF]

Bull.Austral.Math.Soc.,Vol.70(2004),177-198, 2007
We study some sub-Riemannian objects (such as horizontal connectivity, horizontal connection, horizontal tangent plane, horizontal mean curvature) in hypersurfaces of sub-Riemannian manifolds. We prove that if a connected hypersurface in a contact manifold of dimension more than three is noncharacteristic or with isolated characteristic points, then ...
arxiv  

Submanifold Geometry in Symmetric Spaces

, 1995
The classical local invariants of a submanifold in a space form are the first fundamental form, the shape operators and the induced normal connection, and they determine the submanifold up to ambient isometry.
C. Terng, G. Thorbergsson
semanticscholar   +1 more source