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Some tools for non-local PDEs from conformal geometry

Dr. Azahara de la Torre Pedraza

Freitag, 2020-10-23 11:30Uhr

In this talk I will explain some new tools developed in conformal geometry to solve non-local elliptic semi-linear equations. These tools originally arose to study geometric properties. However, since they are analytic tools, they help us not only to solve geometric problems, but also several non-local / non-linear PDE problems (through the understanding of the instrinsic geometry which is present in the PDEs). Conformal geometry has been traditionally developed to deal with the study of scalar curvature (the natural generalization of the Gauss curvature to higher dimension), but this new approach (from a non-local point of view) leads to the study of other generalizations of the Gauss curvature, such as the Q-curvature. Moreover, these tools are useful to study di↵erent equations, functionals and extremal solutions for inequalities arising in non-local geometric analysis. Would it be possible to use them for studying the extrinsic non-local geometry as well?