EuDML | Browse

Based on conjugate duality we construct several gap functions for general variational inequalities and equilibrium problems, in the formulation of which a so-called perturbation function is used. These functions are written with the help of the Fenchel-Moreau conjugate of the functions involved. In case we are working in the convex setting and a regularity condition is fulfilled, these functions become gap functions. The techniques used are the ones considered in [Altangerel L., Boţ R.I., Wanka...

Ricci flow coupled with harmonic map flow

Reto Müller (2012)

Annales scientifiques de l'École Normale Supérieure

We investigate a coupled system of the Ricci flow on a closed manifold $M$ with the harmonic map flow of a map $φ$ from $M$ to some closed target manifold $N$ , $\frac{\partial}{\partial t} g = - 2 Rc + 2 α \nabla φ \otimes \nabla φ, \frac{\partial}{\partial t} φ = τ_{g} φ,$ where $α$ is a (possibly time-dependent) positive coupling constant. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of $φ$ a-priori by choosing $α$ large enough. Moreover, it suffices to bound the curvature of $(M, g (t))$ to also obtain control of ...

Riemannian geometries on spaces of plane curves

Peter W. Michor, David Mumford (2006)

Journal of the European Mathematical Society

We study some Riemannian metrics on the space of smooth regular curves in the plane, viewed as the orbit space of maps from $S^{1}$ to the plane modulo the group of diffeomorphisms of $S^{1}$ , acting as reparametrizations. In particular we investigate the metric, for a constant $A > 0$ , $G_{c}^{A} (h, k) : = \int_{S^{1}} (1 + A κ_{c} {(θ)}^{2}) 〈 h (θ), k (θ) 〉 | c^{'} (θ) | d θ$ where $κ_{c}$ is the curvature of the curve $c$ and $h$ , $k$ are normal vector fields to $c$ . The term $A κ^{2}$ is a sort of geometric Tikhonov regularization because, for $A = 0$ , the geodesic distance between any two distinct curves is 0, while for $A > 0$ the...

Right closing almost conjugacy for G-shifts of finite type

Andrew Dykstra (2006)

Colloquium Mathematicae

A G-shift of finite type (G-SFT) is a shift of finite type which commutes with the continuous action of a finite group G. For irreducible G-SFTs we classify right closing almost conjugacy, answering a question of Bill Parry.

Rigidity and gluing for Morse and Novikov complexes

Octav Cornea, Andrew Ranicki (2003)

Journal of the European Mathematical Society

We obtain rigidity and gluing results for the Morse complex of a real-valued Morse function as well as for the Novikov complex of a circle-valued Morse function. A rigidity result is also proved for the Floer complex of a hamiltonian defined on a closed symplectic manifold $(M, ω)$ with $c_{1} {|_{π_{2} (M)} = [ω] |}_{π_{2} (M)} = 0$ . The rigidity results for these complexes show that the complex of a fixed generic function/hamiltonian is a retract of the Morse (respectively Novikov or Floer) complex of any other sufficiently $C^{0}$ close generic function/hamiltonian....

Rigidity of Furstenberg entropy for semisimple Lie group actions

Amos Nevo, Robert J. Zimmer (2000)

Annales scientifiques de l'École Normale Supérieure

Rigidity of group actions

Masahiko Kanai (1996/1997)

Séminaire de théorie spectrale et géométrie

Currently displaying 21 – 40 of 43

Previous Page 2 Next