Geometric Applications of Fourier Series and Spherical HarmonicsThis is the first comprehensive exposition of the application of spherical harmonics to prove geometric results. The author presents all the necessary tools from classical theory of spherical harmonics with full proofs. Groemer uses these tools to prove geometric inequalities, uniqueness results for projections and intersection by planes or half spaces, stability results, and characterizations of convex bodies of a particular type, such as rotors in