The elliptic boundary conditions for different bundles and geometries

Antoni Pierzchalski (Lodz)
Analysis Seminar
Thursday, 1 November, 2018, at 16:15-17:00, in Aud. D3 (1531-215)

We are going to review some recent results on the ellipticity at the boundary of the Laplace type operators. In the Riemannian case we will focus on the bundle of symmetric tensors and, in particular, investigate two elliptic operators: divgrad the Sampson Laplacian. We will relate them to the Lichnerowicz Laplacian and show the contrast to the skew-symmetric case. In the symplectic case we will review the boundary behavior of the Laplace type operators defined recently by L-S. Tseng, L. Wang and S-T Yau for the bundle of primitive forms. We will recall the construction of elliptic complexes in this case and discuss some natural boundary conditions there. (Joint work with Anna Kimaczyńska.)

Contact person: Bent Ørsted