Advances in Nonlinear Analysis (Sep 2024)

The second Yamabe invariant with boundary

  • Ho Pak Tung,
  • Pyo Juncheol

DOI
https://doi.org/10.1515/anona-2024-0039
Journal volume & issue
Vol. 13, no. 1
pp. 377 – 412

Abstract

Read online

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.

Keywords