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Displaying 141 – 160 of 300

Means in complete manifolds: uniqueness and approximation

Marc Arnaudon, Laurent Miclo (2014)

ESAIM: Probability and Statistics

Let M be a complete Riemannian manifold, M ∈ ℕ and p ≥ 1. We prove that almost everywhere on x = (x1,...,xN) ∈ MN for Lebesgue measure in MN, the measure $μ (x) = N \sum_{k = 1}^{N} x_{k}$ μ ( x ) = 1 N ∑ k = 1 N δ x k has a uniquep–mean ep(x). As a consequence, if X = (X1,...,XN) is a MN-valued random variable with absolutely continuous law, then almost surely μ(X(ω)) has a unique p–mean. In particular if (Xn)n ≥ 1 is an independent sample of an absolutely continuous law in M, then the process ep,n(ω) = ep(X1(ω),...,Xn(ω)) is...

Meilleures constantes dans le théorème d'inclusion de Sobolev

Emmanuel Hebey, Michel Vaugon (1996)

Annales de l'I.H.P. Analyse non linéaire

Meilleures constantes et inégalités de Sobolev optimales sur les variétés riemanniennes compactes

Emmanuel Hebey (1997/1998)

Séminaire de théorie spectrale et géométrie

Metric Ricci Curvature and Flow for PL Manifolds

Emil Saucan (2013)

Actes des rencontres du CIRM

We summarize here the main ideas and results of our papers [28], [14], as presented at the 2013 CIRM Meeting on Discrete curvature and we augment these by bringing up an application of one of our main results, namely to solving a problem regarding cube complexes.

Metric tensor estimates, geometric convergence, and inverse boundary problems.

Anderson, Michael, Katsuda, Atsushi, Kurylev, Yaroslav, Lassas, Matti, Taylor, Michael (2003)

Electronic Research Announcements of the American Mathematical Society [electronic only]

Metrics of constant curvature on a Riemann surface with two corners on the boundary

Jürgen Jost, Guofang Wang, Chunqin Zhou (2009)

Annales de l'I.H.P. Analyse non linéaire

Metrics with Harmonic Spinors.

C. Bär (1996)

Geometric and functional analysis

Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity

Stefanov, Plamen (2008)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 53C24, 53C65, 53C21.This is a survey of the recent results by the author and Gunther Uhlmann on the boundary rigidity problem and on the associated tensor tomography problem.Author partly supported by NSF Grant DMS-0400869.

Minimal submanifolds in $ℝ^{4}$ with a g.c.K. structure

Marian-Ioan Munteanu (2008)

Czechoslovak Mathematical Journal

In this paper we obtain all invariant, anti-invariant and $C R$ submanifolds in $(ℝ^{4}, g, J)$ endowed with a globally conformal Kähler structure which are minimal and tangent or normal to the Lee vector field of the g.c.K. structure.

Minimal surfaces, the Dirac operator and the Penrose inequality

Marc Herzlich (2001/2002)

Séminaire de théorie spectrale et géométrie

Minoration du spectre des variétés hyperboliques de dimension 3

Pierre Jammes (2012)

Bulletin de la Société Mathématique de France

Soit $M$ une variété hyperbolique compacte de dimension 3, de diamètre $d$ et de volume $\leq V$ . Si on note $μ_{i} (M)$ la $i$ -ième valeur propre du laplacien de Hodge-de Rham agissant sur les 1-formes coexactes de $M$ , on montre que $μ_{1} (M) \geq \frac{c}{d^{3} e^{2 k d}}$ et $μ_{k + 1} (M) \geq \frac{c}{d^{2}}$ , où $c > 0$ est une constante ne dépendant que de $V$ , et $k$ est le nombre de composantes connexes de la partie mince de $M$ . En outre, on montre que pour toute 3-variété hyperbolique $M_{\infty}$ de volume fini avec cusps, il existe une suite $M_{i}$ de remplissages compacts de $M_{\infty}$ , de diamètre $d_{i} \to + \infty$ telle que et $μ_{1} (M_{i}) \geq \frac{c}{d_{i}^{2}}$ .

Minorations sur le $λ_{1}$ des variétés riemanniennes

Sylvestre Gallot (1980/1981)

Séminaire Bourbaki

Moduli space, heights and isospectral sets of metrics

R. Phillips (1989/1990)

Séminaire Équations aux dérivées partielles (Polytechnique)

Monge-Ampère equations and surfaces with negative Gaussian curvature

Mikio Tsuji (1997)

Banach Center Publications

In [24], we studied the singularities of solutions of Monge-Ampère equations of hyperbolic type. Then we saw that the singularities of solutions do not coincide with the singularities of solution surfaces. In this note we first study the singularities of solution surfaces. Next, as the applications, we consider the singularities of surfaces with negative Gaussian curvature. Our problems are as follows: 1) What kinds of singularities may appear?, and 2) How can we extend the surfaces beyond the singularities?...

Monogenic functions in conformal geometry.

Eastwood, Michael, Ryan, John (2007)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Monopole metrics and the orbifold Yamabe problem

Jeff A. Viaclovsky (2010)

Annales de l’institut Fourier

We consider the self-dual conformal classes on $n # {ℂℙ}^{2}$ discovered by LeBrun. These depend upon a choice of $n$ points in hyperbolic $3$ -space, called monopole points. We investigate the limiting behavior of various constant scalar curvature metrics in these conformal classes as the points approach each other, or as the points tend to the boundary of hyperbolic space. There is a close connection to the orbifold Yamabe problem, which we show is not always solvable (in contrast to the case of compact manifolds)....

Monotone point-to-set vector fields.

da Cruz Neto, J.X., Ferreira, O.P., Lucambio Pérez, L.R. (2000)

Balkan Journal of Geometry and its Applications (BJGA)

Morse indices of Yang-Mills connections over the unit sphere

Shin Nayatani, Hajime Urakawa (1995)

Compositio Mathematica

Multiplicity results for the prescribed scalar curvature on low spheres

Mohamed Ben Ayed, Mohameden Ould Ahmedou (2008)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

In this paper, we consider the problem of multiplicity of conformal metrics of prescribed scalar curvature on standard spheres $𝕊^{3}, 𝕊^{4}$ . Under generic conditions we establish someMorse Inequalities at Infinity, which give a lower bound on the number of solutions to the above problem in terms of the total contribution of its critical points at Infinityto the difference of topology between the level sets of the associated Euler-Lagrange functional. As a by-product of our arguments we derive a new existence...

Non Existence and Existence of Capillary Surfaces.

Robert Finn, Enrico Giusti (1979)

Manuscripta mathematica

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