Hilbert's talk at the second International Congress of 1900 in
Paris marked the beginning of a new era in the calculus of
variations. A development began which, within a few decades,
brought tremendous success, highlighted by the 1929 theorem of
Ljusternik and Schnirelman on the existence of three distinct prime
closed geodesics on any compact surface of genus zero, and the
1930/31 solution of Plateau's problem by Douglas and Rado. The book
gives a concise introduction to variational methods and presents an
overview of areas of current research in the field.
The fourth edition gives a survey on new developments in the
field. In particular it includes the proof for the convergence of
the Yamabe flow and a detailed treatment of the phenomenon of
blow-up. Also the recently discovered results for backward bubbling
in the heat flow for harmonic maps or surfaces are discussed. Aside
from these more significant additions, a number of smaller changes
throughout the text have been made and the references have been
updated."
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