Seminario Azahara de la Torre Pedraza Titolo: Non-local ODE's methods arising in conformal Geometry

Martedì, 5 Ottobre, 2021 - 15:30

Martedì 5 ottobre alle ore 15.30 si terrà in Sala di Consiglio e via Meet il seminario di Dipartimento della dott.ssa Azahara de la Torre Pedraza in vista della chiamata da RTDB nel settore scienti co Disciplinare

In this talk I will explain some new tools developed in conformal geometry to solve non-local elliptic semilinear 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 nonlocal point of view) leads to the study of other generalizations of the Gauss curvature, such as the Qcurvature. 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?

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