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Global existence of solutions to Schrödinger equations on compact riemannian manifolds below H 1

Sijia Zhong (2010)

Bulletin de la Société Mathématique de France

In this paper, we will study global well-posedness for the cubic defocusing nonlinear Schrödinger equations on the compact Riemannian manifold without boundary, below the energy space, i.e. s < 1 , under some bilinear Strichartz assumption. We will find some s ˜ < 1 , such that the solution is global for s > s ˜ .

Global generalized Bianchi identities for invariant variational problems on gauge-natural bundles

Marcella Palese, Ekkehart Winterroth (2005)

Archivum Mathematicum

We derive both local and global generalized Bianchi identities for classical Lagrangian field theories on gauge-natural bundles. We show that globally defined generalized Bianchi identities can be found without the a priori introduction of a connection. The proof is based on a global decomposition of the variational Lie derivative of the generalized Euler-Lagrange morphism and the representation of the corresponding generalized Jacobi morphism on gauge-natural bundles. In particular, we show that...

Global left loop structures on spheres

Michael K. Kinyon (2000)

Commentationes Mathematicae Universitatis Carolinae

On the unit sphere 𝕊 in a real Hilbert space 𝐇 , we derive a binary operation such that ( 𝕊 , ) is a power-associative Kikkawa left loop with two-sided identity 𝐞 0 , i.e., it has the left inverse, automorphic inverse, and A l properties. The operation is compatible with the symmetric space structure of 𝕊 . ( 𝕊 , ) is not a loop, and the right translations which fail to be injective are easily characterized. ( 𝕊 , ) satisfies the left power alternative and left Bol identities “almost everywhere” but not everywhere....

Global minimizers for axisymmetric multiphase membranes

Rustum Choksi, Marco Morandotti, Marco Veneroni (2013)

ESAIM: Control, Optimisation and Calculus of Variations

We consider a Canham − Helfrich − type variational problem defined over closed surfaces enclosing a fixed volume and having fixed surface area. The problem models the shape of multiphase biomembranes. It consists of minimizing the sum of the Canham − Helfrich energy, in which the bending rigidities and spontaneous curvatures are now phase-dependent, and a line tension penalization for the phase interfaces. By restricting attention to axisymmetric surfaces and phase distributions, we extend our previous...

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