Abstract
New inequalities for certain Green's functions are given. They may be interpreted physically in many ways, for example, as applying to the quantum mechanical motion of a particle in a potential or to diffusion in the presence of absorbers. These inequalities involve a symmetrization process very closely related to Steiner symmetrization used in the theory of isoperimetric inequalities. The usual geometrical and physical isoperimetric inequalities are very special cases of our general inequality (3.9), arising when the potential is taken to be a characteristic function of a bounded domain and the ``time'' in the Green's function is allowed to get very large or very small.
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