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Bounding the invariant spectrum when the scalar curvature is non-negative
Stuart James Hall, Thomas Murphy
On compact Riemannian manifolds with a large isometry group we investigate the invariant spectrum of the ordinary Laplacian. For either a toric Kaehler metric, or a rotationally-sy…
Compact Hermitian symmetric spaces, coadjoint orbits, and the dynamical stability of the Ricci flow
Stuart James Hall, Thomas Murphy, James Waldron
Using a stability criterion due to Kröncke, we show, providing , the Kähler--Einstein metric on the Grassmannian of complex -planes in an $n…
Numerically destabilizing minimal discs
Nicholas Brubaker, Thomas Murphy, K. Oskar Negron
When calculating the index of a minimal surface, the set of smooth functions on a domain with compact support is the standard setting to describe admissible variations. We show tha…
Bounding the first invariant eigenvalue of toric Kähler manifolds
Stuart James Hall, Thomas Murphy
We generalise a theorem of Engman and Abreu--Freitas on the first invariant eigenvalue of non-negatively curved -invariant metrics on to general toric Kähl…
Conformally Kähler geometry and quasi-Einstein metrics
Wafaa Batat, Stuart James Hall, Ali Jizany +1
We prove that the quasi-Einstein metrics found by Lü, Page and Pope on -bundles over Fano Kähler-Einstein bases are conformally Kähler and that the Kähler class of…