Ricci flows, wormholes and critical phenomena

We study the evolution of wormhole geometries under Ricci flow using numerical methods. Depending on values of initial data parameters, wormhole throats either pinch off or evolve to a monotonically growing state. The transition between these two behaviors exhibits a from of critical phenomena reminiscent of that observed in gravitational collapse. Similar results are obtained for initial data that describe space bubbles attached to asymptotically flat regions. Our numerical methods are applicable to "matter-coupled" Ricci flows derived from conformal invariance in string theory.Comment: 8 pages, 5 figures. References added and minor changes to match version accepted by CQG as a fast track communicatio

Ursinus College Bulletin Vol. 10, No. 4, January 1894

A digitized copy of the January 1894 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1091/thumbnail.jp

Ursinus College Bulletin Vol. 10, No. 3, December 1893

A digitized copy of the December 1893 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1090/thumbnail.jp

Ursinus College Bulletin Vol. 10, No. 2, November 1893

A digitized copy of the November 1893 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1089/thumbnail.jp

Ursinus College Bulletin Vol. 10, No. 7, April 1894

A digitized copy of the April 1894 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1094/thumbnail.jp

Ursinus College Bulletin Vol. 10, No. 5, February 1894

A digitized copy of the February 1894 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1092/thumbnail.jp

Ursinus College Bulletin Vol. 10, No. 6, March 1894

A digitized copy of the March 1894 Ursinus College Bulletin.https://digitalcommons.ursinus.edu/ucbulletin/1093/thumbnail.jp

Singularity Formation in 2+1 Wave Maps

We present numerical evidence that singularities form in finite time during the evolution of 2+1 wave maps from spherically equivariant initial data of sufficient energy.Comment: 5 pages, 3 figure

Conformally flat black hole initial data, with one cylindrical end

We give a complete analytical proof of existence and uniqueness of extreme-like black hole initial data for Einstein equations, which possess a cilindrical end, analogous to extreme Kerr, extreme Reissner Nordstrom, and extreme Bowen-York's initial data. This extends and refines a previous result \cite{dain-gabach09} to a general case of conformally flat, maximal initial data with angular momentum, linear momentum and matter.Comment: Minor changes and formula (21) revised according to the published version in Class. Quantum Grav. (2010). Results unchange

The Tulczyjew triple for classical fields

The geometrical structure known as the Tulczyjew triple has proved to be very useful in describing mechanical systems, even those with singular Lagrangians or subject to constraints. Starting from basic concepts of variational calculus, we construct the Tulczyjew triple for first-order Field Theory. The important feature of our approach is that we do not postulate {\it ad hoc} the ingredients of the theory, but obtain them as unavoidable consequences of the variational calculus. This picture of Field Theory is covariant and complete, containing not only the Lagrangian formalism and Euler-Lagrange equations but also the phase space, the phase dynamics and the Hamiltonian formalism. Since the configuration space turns out to be an affine bundle, we have to use affine geometry, in particular the notion of the affine duality. In our formulation, the two maps $\alpha$ and $\beta$ which constitute the Tulczyjew triple are morphisms of double structures of affine-vector bundles. We discuss also the Legendre transformation, i.e. the transition between the Lagrangian and the Hamiltonian formulation of the first-order field theor