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The aim of this book is to present different aspects of the deep
interplay between Partial Differential Equations and Geometry. It
gives an overview of some of the themes of recent research in the
field and their mutual links, describing the main underlying ideas,
and providing up-to-date references.Collecting together the lecture
notes of the five mini-courses given at the CIME Summer School held
in Cetraro (Cosenza, Italy) in the week of June 19-23, 2017, the
volume presents a friendly introduction to a broad spectrum of
up-to-date and hot topics in the study of PDEs, describing the
state-of-the-art in the subject. It also gives further details on
the main ideas of the proofs, their technical difficulties, and
their possible extension to other contexts. Aiming to be a primary
source for researchers in the field, the book will attract
potential readers from several areas of mathematics.
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