Extrinsic eigenvalues upper bounds for submanifolds in weighted manifolds

EXTRINSIC UPPER BOUNDS THE FIRST EIGENVALUE OF THE p-STEKLOV PROBLEM ON SUBMANIFOLDS

“…They also proved analogue inequalities involving higher order mean curvatures like in (2). Recently, both the authors with Manfio have extended this inequality for submanifolds of any Riemannian manifold of bounded sectional curvature in [14].…”

“…Finally, we recall the following technical lemma proved by Manfio and the two authors in [14] which will be useful at the end of the proof of Theorem 1.1.…”

REILLY-TYPE UPPER BOUNDS FOR THE p-STEKLOV PROBLEM ON SUBMANIFOLDS

“…Finally, we recall the following technical lemma proved by Manfio and the authors in [15] which will be useful at the end of the proof of Theorem 1.1. LEMMA 2.4 [15].…”

“…Finally, we recall the following technical lemma proved by Manfio and the authors in [15] which will be useful at the end of the proof of Theorem 1.1. LEMMA 2.4 [15]. Let ( MN , ḡ) be a Riemannian manifold with sectional curvature bounded from above by δ, δ > 0.…”

“…They also proved analogous inequalities involving higher order mean curvatures as in (1.2). Recently, Manfio and the authors have extended this inequality for submanifolds of any Riemannian manifold of bounded sectional curvature in [15].…”