Ben Sharp

I'm a lecturer in analysis at the University of Leeds and the main focus of my research is related to PDE coming from geometry. In particular those associated with harmonic maps (and generalisations thereof), minimal submanifolds and Willmore surfaces.

Publications and Preprints

Look for my papers on the Arxiv

  1. CMC hypersurfaces with bounded Morse index Joint with Theodora Bourni and Giuseppe Tinaglia. Preprint 2021
  2. Łojasiewicz inequalities near simple bubble trees Joint with Andrea Malchiodi and Melanie Rupflin. Preprint 2020
  3. Bubbling analysis and geometric convergence results for free boundary minimal surfaces Joint with Lucas Ambrozio, Reto Buzano and Alessandro Carlotto. J. l'École Polytechque - Mathématiques 6 (2019), 621--664
  4. Geometric convergence results for closed minimal surfaces via bubbling analysis Joint with Lucas Ambrozio, Reto Buzano and Alessandro Carlotto. Submitted 2018
  5. Compactness analysis for free boundary minimal hypersurfaces. Joint with Lucas Ambrozio and Alessandro Carlotto. Calc. Var. Partial Differential Equations 57 (2018), no. 1, 57:22
  6. A note on the index of closed minimal hypersurfaces of flat tori. Joint with Lucas Ambrozio and Alessandro Carlotto. Proc. Amer. Math. Soc. 146 (2018), no. 1, 335--344
  7. Index estimates for free boundary minimal hypersurfaces. Joint with Lucas Ambrozio and Alessandro Carlotto Math. Ann. 370 (2018), no. 3-4, 1063--1078
  8. Comparing the Morse index and the first Betti number of minimal hypersurfaces. Joint with Lucas Ambrozio and Alessandro Carlotto J. Differential Geom. 108 (2018), no. 3, 379--410
  9. Qualitative and quantitative estimates for minimal hypersurfaces with bounded index and area. Joint with Reto Buzano Trans. Amer. Math. Soc. 370 (2018) no. 6, 4373--4399
  10. Compactness of the space of minimal hypersurfaces with bounded volume and p-th Jacobi eigenvalue. Joint with Lucas Ambrozio and Alessandro Carlotto. J. Geom. Anal. 26 (2016), no. 4, 2591--2601
  11. Smooth compactness of f-minimal hypersurfaces with bounded f-index. Joint with Ezequiel Barbosa and Yong Wei Proc. Amer. Math. Soc. 145 (2017), no. 11, 4945--4961
  12. Compactness of minimal hypersurfaces with bounded index. J. Differential Geom. 106 (2017), no. 2, 317--339
  13. Global estimates and energy identities for elliptic systems with antisymmetric potentials. Joint with Tobias Lamm Comm. Partial Differential Equations 41 (2016), no. 4, 579--608
  14. Regularity at the free boundary for Dirac-harmonic maps from surfaces. Joint with Miaomiao Zhu Calc. Var. Partial Differential Equations 55 (2016), no. 2, Art. 27, 30 pp
  15. Critical ∂̄ problems in one complex dimension and some remarks on conformally invariant variational problems in two real dimensions. Adv. Calc. Var. 7 (2014), no. 3, 353--378
  16. Higher integrability for solutions to a system of critical elliptic PDE. Methods. Appl. Anal., 21 (2014) No. 2, 221--240
  17. Decay Estimates for Rivière's equation with applications to regularity and compactness. Joint with Peter Topping. Trans. Amer. Math. Soc. 365 (2013), no. 5, 2317--2339
  18. Compensation Phenomena in Geometric Partial Differential Equations. Ph.D Thesis 2012

Recent and upcoming talks/academic visits

Teaching

Seminars and events I have co-organised