The book presents a comprehensive exposition of extension results
for maps between different geometric objects and of extension-trace
results for smooth functions on subsets with no a priori
differential structure (Whitney problems). The account covers
development of the area from the initial classical works of the
first half of the 20th century to the flourishing period of the
last decade. Seemingly very specific these problems have been from
the very beginning a powerful source of ideas, concepts and methods
that essentially influenced and in some cases even transformed
considerable areas of analysis. Aside from the material linked by
the aforementioned problems the book also is unified by geometric
analysis approach used in the proofs of basic results. This
requires a variety of geometric tools from convex and combinatorial
geometry to geometry of metric space theory to Riemannian and
coarse geometry and more. The necessary facts are presented mostly
with detailed proofs to make the book accessible to a wide
audience.
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