= Method of descent for the wave equation
Extend lower-dimensional data independently of an extra coordinate and apply the higher-dimensional <wave equation> solution. Projecting a three-dimensional sphere to the planar disk yields the <kernel> $[2\pi\sqrt{t^2-r^2}]^{-1}$ for the two-dimensional solution with zero initial displacement. This <method of descent for the wave equation> explains why three-dimensional wave propagation can depend on a sphere while two-dimensional propagation depends on its interior.
Back to article page
