Geometric Analysis combines differential equations with
differential geometry. An important aspect of geometric analysis is
to approach geometric problems by studying differential equations.
Besides some known linear differential operators such as the
Laplace operator, many differential equations arising from
differential geometry are nonlinear. A particularly important
example is the Monge-Ampere equation. Applications to geometric
problems have also motivated new methods and techniques in
differential equations. The field of geometric analysis is broad
and has had many striking applications. This handbook of geometric
analysis presents introductions and survey papers treating
important topics in geometric analysis, with their applications to
related fields. It can be used as a reference by graduate students
and by researchers in related areas.
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