26 04 im alumniV8
22 11 im fatiado face
22 11 im fatiado twitter
22 11 im fatiado youtube
22 11 im fatiado gmail
22 11 im fatiado brazil
22 11 im fatiado england
22 11 im fatiado spain

03 01 IM HarmonicFunctions NoticiaTítulo: Harmonic functions on spaces with Ricci curvature bounded below

Palestrante: Jesús Núñez-Zimbrón (CIMAT)

Data: 04/01/2022
Horário: 14:00h
Local: Transmissão online

Confira AQUI o link para a transmissão.
ID da reunião: 811 6291 5241 

Resumo:The so-called spaces with the Riemannian curvature-dimension conditions (RCD spaces) are metric measure spaces which are not necessarily smooth but admit a notion of “Ricci curvature bounded below and dimension bounded above”. These spaces arise naturally as Gromov-Hausdorff limits of Riemannian manifolds with these conditions and, in contrast to manifolds, RCD spaces typically have topological or metric singularities. Nevertheless a considerable amount of Riemannian geometry can be recovered for these spaces. In this talk I will present recent work joint with Guido De Phillipis, in which we show that the gradients of harmonic functions vanish at the singular points of the space. I will mention two applications of this result on smooth manifolds: it implies that there does not exist an a priori estimate on the modulus of continuity of the gradient of harmonic functions depending only on lower bounds of the sectional curvature and there is no a priori Calderón-Zygmund inequality for the Laplacian with bounds depending only on the sectional curvature.

Mais informação sobre a palestra, seminários futuros e passados pode ser encontradas AQUI.