Analysis Learning Seminar
Gradients on Higher Dimensional Sierpinski Gaskets
Gamal Mograby (University of Connecticut)
Friday, December 7, 2018
MONT 414 (Storrs)
In recent years a theory of analysis on fractals was extensively developed. A central concept in this theory is Dirichlet forms, which have the advantage of providing concrete descriptions of harmonic functions, Green's functions and Laplacian on spaces without a priori smooth structure.
In this talk, we will introduce Gradients following Teplyaev approach. We will avoid general concepts and explain the ideas on concrete fractals like the higher dimensional Sierpinski Gaskets. Moreover, we show how to construct a measurable Riemannian structure on such fractals and relate it to the definition of Gradients. In the last part of the talk, we will introduce our results generalizing some of Teplyaev existence and continuity statements of Gradients on higher dimensional Sierpinski Gaskets.