Title: The asymptotic behavior of eigenfunctions on symmetric spacesAbstract: Let X be a compact locally symmetric space, and Y a locally symmetric subspace.  Let f be an eigenfunction of the invariant differential operators on X with eigenvalue tending to infinity.  I will present bounds for the period and Fourier coefficients of f along Y, and […]

Title: A fourth-order Escobar-Yamabe problem on a half-ballAbstract: The celebrated Yamabe problem asks us to make a conformal change on a compact Riemannian manifold such that the scalar curvature becomes constant. The (Type-II) Escobar-Yamabe problem is to make a conformal change on a compact Riemannian manifold with boundary so that the scalar curvature vanishes and […]