Noticias en español
Mixed Local and Nonlocal Laplacian without Standard Critical Exponent for Lane-Emden equation
Abstract: —–see attached
Read MoreEvolution of viscous vortex filaments.
Abstract: Vorticity filaments (one-dimensional structures where vorticity concentrates) play a central role in understanding turbulence generation and energy transfer in fluids. In this talk, I will discuss about how these structures evolve in a viscous fluid. I will consider initial data given by a vorticity measure supported on an infinite smooth curve in R^3. I will show that, for short enough time, the solution consists of a leading-order Lamb–Oseen vortex centered around a curve that evolves according to the binormal flow, a second-order term reflecting the local curvature of the...
Read MoreRenormalized Volume/Area from Conformal Gravity
Abstract: We introduce a mechanism (Conformal Renormalization) to cancel divergences in Einstein gravity for asymptotically hyperbolic Einstein (AHE) spaces. In the bulk, the procedure amounts to embedding Einstein gravity in Conformal Gravity, whose action is given by a conformal invariant in four dimensions. This scheme is proved to be equivalent to both holographic techniques (for physicists) and the notion of Renormalized Volume (for mathematicians). In turn, for surfaces anchored to the conformal boundary of AHE spaces, its area and other co-dimension 2 functionals also exhibit a...
Read MoreFinding (many) prescribed mean curvature surfaces in the presence of a strictly stable minimal surfaces.
Abstract: In the last decades, there has been fascinating progress in the variational theory for the area functional – that is, the codimension 1 volume – using tools from PDEs and Geometric Measure Theory, and in connection with the problem of finding prescribed mean curvature (PMC) hypersurfaces. In this talk, we describe some recent contributions from joint work with Jared Marx-Kuo (Rice University) in which we construct infinitely many PMCs for a large class of prescribing functions in a compact Riemannian manifold containing a strictly stable minimal hypersurface.
Read MoreThe Korteweg-de Vries on the general star graphs
Abstract: In this talk, we discuss local well-posedness for the Cauchy problem associated with the Korteweg-de Vries (KdV) equation on a general metric star graph. The graph comprises (m+k) semi-infinite edges: k negative half-lines and m positive half-lines, all joined at a common vertex. The choice of boundary conditions is compatible with the conditions determined by the semigroup theory. The crucial point in this work is to obtain the integral formula using the forcing operator method. This work extends the previous results obtained by [2018 Cavalcante] for the specific case of the...
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