Yamabe problem on compact manifolds with boundary

We proved the existence of conformal metric with nonzero constant scalar curvature and nonzero constant boundary mean curvature under some natural conditions. We also solved some remaining cases left open by J. Escobar. Furthermore, we establish the compactness of minimizers which led to a partial affirmative answer to the Han-Li conjecture. We also studied one types of Yamabe flow on compact manifolds with boundary, which has mean curvature equals to zero on the boundary. Convergence of flow is established under some conditions. In another work, We studied the classification of nonnegative solutions to polyharmonic functions with conformally invariant boundary conditions. We proved that nonnegative solutions of that elliptic equations have to be of the ``polynomials plus bubbles" form. The presence of a polynomial part is a new phenomenon.Ph.D.Includes bibliographical referencesby Liming Su