Algebra & Number Theory publishes high-quality original research articles in algebra and number theory, interpreted broadly, for example including algebraic and arithmetic geometry.
Analysis & PDE publishes high-quality original research in all areas of mathematical analysis and partial differential equations. The field is interpreted broadly and, and for example, includes topics such as harmonic analysis, operator algebras, index theory, and analytic aspects of mathematical physics.
We establish universal inequalities for the eigenvalues of the clamped plate problem on compact submanifolds of Euclidean space, of spheres and of real, complex and quaternionic projective spaces. We prove similar results for the biharmonic operator on domains of Riemannian manifolds that admit spherical eigenmaps (this includes compact homogeneous Riemannian spaces) and finally on domains of hyperbolic space.