5 citations · 10 across the 13 of their papers we have counts for
14 papers · 1 filter
Deformed Hermitian-Yang-Mills equation on the manifold of full flags
Benoit Charbonneau, Gonçalo Oliveira, Rosa Sena-Dias
We construct the first example of a higher rank, irreducible deformed Hermitian-Yang-Mills (dHYM) connection in the small radius regime. We also construct these in the large radius…
Hermitian, Ricci-flat toric metrics on non-compact surfaces à la Biquard-Gauduchon
Gonçalo Oliveira, Rosa Sena-Dias
Biquard-Gauduchon have shown that conformally Kähler, Ricci-flat, ALF toric metrics on the complement of toric divisors are: the Taub-NUT metric with reversed orientation, in the K…
Scalar-flat Kähler metrics with varying cone angle singularities along a divisor
Gonçalo Oliveira, Rosa Sena-Dias
Using an ansatz due to LeBrun we construct complete scalar-flat Kähler metrics with a prescribed varying conical singularity along a divisor.
Einstein metrics from the Calabi ansatz via Derdziński duality
Gonçalo Oliveira, Rosa Sena-Dias
Drawing on results of Derdziński's from the 80's, we classify conformally Kähler, -invariant, Einstein metrics on the total space of , for all $m \in \mathbb…
Minimal Lagrangian tori and action-angle coordinates
Gonçalo Oliveira, Rosa Sena-Dias
We investigate which orbits of an -dimensional torus action on a -dimensional toric Kähler manifold are minimal. In other words, we study minimal submanifolds appearing…
Uniqueness among scalar-flat Kähler metrics on non-compact toric -manifolds
Rosa Sena-Dias
Abreu-Sena-Dias have constructed two distinct families of scalar-flat Kähler non-compact toric metrics using Donaldson's rephrasing of Joyce's construction in action-angle coordina…
Critical Kahler toric metrics for the invariant first eigenvalue
Rosa Sena-Dias
In [LS], it is shown shown that the first eigenvalue of the Laplacian restricted to the space of invariant functions on a toric Kähler manifold (i.e. , the invarian…
Recovering -invariant toric Kähler metrics on from the torus equivariant spectrum
Tomás A. Reis, Rosa Sena-Dias
In this note we prove that toric Kähler metrics on complex projective space which are also -invariant are determined by their equivariant spectrum i.e. the list of eigenvalue…
Toric aspects of the first eigenvalue
Eveline Legendre, Rosa Sena-Dias
In this paper we study the smallest non-zero eigenvalue of the Laplacian on toric Kähler manifolds. We find an explicit upper bound for in terms of moment polytope data…
Curvature of scalar-flat Kahler metrics on non-compact symplectic toric 4-manifolds
Rosa Sena-Dias
In this paper, we show that the complete scalar-flat Kahler metrics constructed by Abreu and the author on strictly unbounded toric 4-dimensional orbifolds have finite norm o…
Equivariant inverse spectral theory and toric orbifolds
Emily B. Dryden, Victor Guillemin, Rosa Sena-Dias
Let O be a symplectic toric 2n-dimensional orbifold with a fixed T^n-action and with a toric Kahler metric g. We previously explored whether, when O is a manifold, the equivariant…
Scalar-flat Kahler metrics on non-compact symplectic toric 4-manifolds
Miguel Abreu, Rosa Sena-Dias
In a recent paper Donaldson explains how to use an older construction of Joyce to obtain four dimensional local models for scalar-flat Kahler metrics with a 2-torus symmetry. Using…
Hearing Delzant polytopes from the equivariant spectrum
Emily B. Dryden, Victor Guillemin, Rosa Sena-Dias
Let M^{2n} be a symplectic toric manifold with a fixed T^n-action and with a toric Kähler metric g. Abreu asked whether the spectrum of the Laplace operator on $\mathcal{C}^\…
Spectral measures on toric varieties and the asymptotic expansion of Tian-Yau-Zelditch
Rosa Sena-Dias
We extend a recent result of Burns, Guillemin and Uribe on the asymptotics of the spectral measure for the reduction metric on a toric variety to any toric metric on a toric variet…