Abtract:We consider on arbitrary Riemannian manifolds the Leibenson equation:$\partial _{t}u=\Delta _{p}u^{q}.$This equation comes from hydrodynamics where it describes filtration of a turbulent compressible liquid in porous medium. Here $u(x,t)$ is the fraction of the volume that the liquid takes in porous medium at time $t$ at point $x$. The parameter $p$ characterizes the turbulence of a...
Differential Geometry SeminarOrganizers:Jialong Deng, Akito FutakiSpeaker:Lucas Ambrozio (IMPA)Time:Tues., 21:00-22:00, Nov. 26, 2024Title:Riemannian manifolds that are determined by their widthsAbstract:A fascinating subject in Geometric Analysis is whether or not a compact Riemannian manifold can be totally reconstructed from the sole knowledge of its Laplace spectrum. Recent development...