https://neckpinch.com/authors/wafaa-batat/New arXiv papers by Wafaa Batat, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/2102.07168/arxiv:2102.07168Sun, 14 Feb 2021 00:00:00 GMTWafaa Batat, Stuart James Hall, Thomas Murphy, James Waldron — We prove that the bi-invariant Einstein metric on SU₂ₙ₊₁ is isolated in the moduli space of Einstein metrics, even though it admits infinitesimal deformations. This gives a non-Kähler, non-product example of this phenomenon adding to the famous example of ℂP}²ⁿ×ℂP}¹ found by Koiso. We apply our methods to derive similar solitonic rigidity results for the Kähler–Einstein metrics on `odd' Grassmannians. We also make explicit a connection between non-integrable deformations and the dynamical instability of metrics under Ricci flow.Ricci flowEinstein metricsKähler geometryStability & uniquenessKähler–Einstein & K-stability https://neckpinch.com/papers/1607.05766/arxiv:1607.05766Tue, 19 Jul 2016 00:00:00 GMTWafaa Batat, Stuart James Hall, Thomas Murphy — The linear stability of warped product Einstein metrics as fixed points of the Ricci flow is investigated. We generalise the results of Gibbons, Hartnoll and Pope and show that in sufficiently low dimensions, all warped product Einstein metrics are unstable. By exploiting the relationship between warped product Einstein metrics, quasi-Einstein metrics and Ricci solitons, we introduce a new destabilising perturbation (the Ricci variation) and show that certain infinite families of warped product Einstein metrics will be unstable in high dimensions.Ricci flowRicci solitonsEinstein metricsAlmost & η-Ricci solitonsStability & uniquenessRotational symmetry & warped products