Advances in Nonlinear Analysis (Sep 2024)
The second Yamabe invariant with boundary
Abstract
Let (M,∂M,g)\left(M,\partial M,g) be a compact Riemannian manifold with boundary. As a generalization of the Yamabe invariant with boundary Y(M,∂M,g)Y\left(M,\partial M,g), we define the kth Yamabe invariant with boundary Yk(M,∂M,g){Y}_{k}\left(M,\partial M,g). We prove some of its properties and study when it can be attained by the generalized metric. We also prove a version of conformal Schwarz lemma on (M,∂M,g)\left(M,\partial M,g) by using the Yamabe flow with boundary.
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