LAUSR.org creates dashboard-style pages of related content for over 1.5 million academic articles. Sign Up to like articles & get recommendations!

Green Function and Self-adjoint Laplacians on Polyhedral Surfaces

Photo by mitchel3uo from unsplash

Abstract Using Roelcke’s formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix… Click to show full abstract

Abstract Using Roelcke’s formula for the Green function, we explicitly construct a basis in the kernel of the adjoint Laplacian on a compact polyhedral surface $X$ and compute the $S$-matrix of $X$ at the zero value of the spectral parameter. We apply these results to study various self-adjoint extensions of a symmetric Laplacian on a compact polyhedral surface of genus two with a single conical point. It turns out that the behaviour of the $S$-matrix at the zero value of the spectral parameter is sensitive to the geometry of the polyhedron.

Keywords: self adjoint; adjoint laplacians; green function; laplacians polyhedral; function self

Journal Title: Canadian Journal of Mathematics
Year Published: 2019

Link to full text (if available)


Share on Social Media:                               Sign Up to like & get
recommendations!

Related content

More Information              News              Social Media              Video              Recommended



                Click one of the above tabs to view related content.