5 citations · 16 across the 6 of their papers we have counts for
6 papers
Global Dynamics, Blow-Up, and Bianchi Cosmology
Nitsan Ben-Gal, Bernhard Brehm, Johannes Buchner +8
Many central problems in geometry, topology, and mathematical physics lead to questions concerning the long-time dynamics of solutions to ordinary and partial differential equation…
Anisotropic Einstein data with isotropic nonnegative scalar curvature
Bernold Fiedler, Juliette Hell, Brian Smith
We construct a black hole initial data for the Einstein equations with prescribed scalar curvature, or more precisely a piece of initial data contained inside the black hole. The c…
Black hole initial data with a horizon of prescribed intrinsic and extrinsic geometry
Brian Smith
The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic and extrinsic geometry. To do this, we us…
Evolution of convex lens-shaped networks under curve shortening flow
Oliver C. Schnürer, Abderrahim Azouani, Marc Georgi +8
We consider convex symmetric lens-shaped networks in R^2 that evolve under curve shortening flow. We show that the enclosed convex domain shrinks to a point in finite time. Further…
Black Hole Initial Data with a Horizon of Prescribed Geometry
Brian Smith
The purpose of this work is to construct asymptotically flat, time symmetric initial data with an apparent horizon of prescribed intrinsic geometry. To do this, we use the paraboli…
Blow-up in the Parabolic Scalar Curvature Equation
Brian Smith
The \textit{parabolic scalar curvature equation} is a reaction-diffusion type equation on an -manifold , the time variable of which shall be denoted by . Given a funct…