All a b c d e f g h i j k l m n o p q r s t u v w x y z Other

Previous Page 46 Next

Displaying 901 – 920 of 1170

Showing per page

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 , ∂ ∂ t g = - 2 Rc + 2 α ∇ φ ⊗ ∇ φ , ∂ ∂ 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 ) : = ∫ 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....

Second variational derivative of local variational problems and conservation laws

Marcella Palese, Ekkehart Winterroth, E. Garrone (2011)

Archivum Mathematicum

We consider cohomology defined by a system of local Lagrangian and investigate under which conditions the variational Lie derivative of associated local currents is a system of conserved currents. The answer to such a question involves Jacobi equations for the local system. Furthermore, we recall that it was shown by Krupka et al. that the invariance of a closed Helmholtz form of a dynamical form is equivalent with local variationality of the Lie derivative of the dynamical form; we remark that...

Currently displaying 901 – 920 of 1170