Results 11 to 20 of about 43,102 (116)

Unimodular measures on the space of all Riemannian manifolds [PDF]

, 2020
We study unimodular measures on the space $\mathcal M^d$ of all pointed Riemannian $d$-manifolds. Examples can be constructed from finite volume manifolds, from measured foliations with Riemannian leaves, and from invariant random subgroups of Lie groups.
Abert, Miklos, Biringer, Ian
core   +2 more sources

Warped Riemannian metrics for location-scale models

, 2017
The present paper shows that warped Riemannian metrics, a class of Riemannian metrics which play a prominent role in Riemannian geometry, are also of fundamental importance in information geometry.
A Terras, AW Knapp, B O’Neill, B Unal, C Atkinson, D Wierstra, DG Luenbeger, E Liao, EH Spanier, EL Lehmann, EP Hsu, F Dobarro, G Cheng, G Gallavotti, GA Young, GJ McLachlan, GN Watson, I Chavel, J Bensadon, JE Marsden, JM Lee, KV Mardia, M Arnaudon, M Arnaudon, M Emery, MP Do Carmo, N Ay, N Ikeda, NN Chentsov, O Kallenberg, P Petersen, PA Absil, PE Kloeden, R. L. Bishop, S Amari, S Helgason, S Lang, S Said, S Said, SI Amari, X Pennec, Y Chikuse, Y Ollivier   +42 more
core   +1 more source

Fourier and Gegenbauer expansions for a fundamental solution of the Laplacian in the hyperboloid model of hyperbolic geometry

, 2012
Due to the isotropy $d$-dimensional hyperbolic space, there exist a spherically symmetric fundamental solution for its corresponding Laplace-Beltrami operator.
Abramowitz M, Andrews G E, Beltrami E, Bers L, Byrd P F, Cohl H S, Cohl H S, Cohl H S, E G Kalnins, Erdélyi A, Erdélyi A, Fano U, Folland G B, Fox L, Gilbarg D, Gradshteyn I S, Grigor’yan A A, Grigor’yan A A, Grigor’yan A A, H S Cohl, Helgason S, Izmest’ev A A, Kalnins E G, Lee J M, Livio M, Losev A G, Magnus W, Morse P M, Olevskii˘ M N, Olver F W J, Olver F W J, Schoen R, Thurston W P, Trudeau R J, Vilenkin N Ja   +34 more
core   +2 more sources

On the total curvature and extrinsic area growth of surfaces with tamed second fundamental form [PDF]

, 2015
In this paper we show that a complete and non-compact surface immersed in the Euclidean space with quadratic extrinsic area growth has finite total curvature provided the surface has tamed second fundamental form and admits total curvature.
Brandao, Cristiane M., Gimeno, Vicent
core   +2 more sources

On Noncommutative and semi-Riemannian Geometry

, 2002
We introduce the notion of a semi-Riemannian spectral triple which generalizes the notion of spectral triple and allows for a treatment of semi-Riemannian manifolds within a noncommutative setting.
Alexander Strohmaier, Baum, Bognar, Cipriani, Connes, Connes, Dixmier, Gracia-Bondia, Hawkins, Kalau, Kastler, Kopf, Landi, O’Neill, Parfionov, Reed, Taylor   +16 more
core   +3 more sources

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

Density‐Valued ARMA Models by Spline Mixtures

Journal of Time Series Analysis, EarlyView.
ABSTRACT This paper proposes a novel framework for modeling time series of probability density functions by extending autoregressive moving average (ARMA) models to density‐valued data. The method is based on a transformation approach, wherein each density function on a compact domain [0,1]d$$ {\left[0,1\right]}^d $$ is approximated by a B‐spline ...
Yasumasa Matsuda, Rei Iwafuchi
wiley   +1 more source

Centrality of star and monotone factorisations

Bulletin of the London Mathematical Society, EarlyView.
Abstract A factorisation problem in the symmetric group is central if conjugate permutations always have the same number of factorisations. We give the first fully combinatorial proof of the centrality of transitive star factorisations that is valid in all genera, which answers a natural question of Goulden and Jackson from 2009.
Jesse Campion Loth, Amarpreet Rattan
wiley   +1 more source

Maximal symplectic torus actions

Bulletin of the London Mathematical Society, EarlyView.
Abstract There are several different notions of maximal torus actions on smooth manifolds, in various contexts: symplectic, Riemannian, complex. In the symplectic context, for the so‐called isotropy‐maximal actions, as well as for the weaker notion of almost isotropy‐maximal actions, we give classifications up to equivariant symplectomorphism.
Rei Henigman
wiley   +1 more source

Fat equator effect and minimality in immersions and submersions of the sphere

Transactions of the London Mathematical Society, Volume 12, Issue 1, December 2025.
Abstract Inspired by the equatorial concentration of measure phenomenon in the sphere, a result which is deduced from the general (and intrinsic), concentration of measure in Sn(1)$\mathbb {S}^n(1)$, we describe in this paper an equatorial concentration of measure satisfied by the closed (compact without boundary), isometric and minimal immersions x:Σm→
Vicent Gimeno i Garcia, Vicente Palmer
wiley   +1 more source