FIRST p-STEKLOV EIGENVALUE UNDER GEODESIC CURVATURE FLOW

Аннотация

We study the first nonzero p-Steklov eigenvalue on a twodimensional compact Riemannian manifold with a smooth boundary along the geodesic curvature flow. We prove that the first nonzero p-Steklov eigenvalue is nondecreasing if the initial metric has positive geodesic curvature on boundary ∂M and vanishing Gaussian curvature in M along the unnormalized
geodesic curvature flow. An eigenvalue estimation is also obtained along the
normalized geodesic curvature flow.