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. Bubbling analysis and geometric convergence results for free boundary minimal surfaces Joint with Lucas Ambrozio, Reto Buzano and Alessandro Carlotto. Submitted 2018
  2. Geometric convergence results for closed minimal surfaces via bubbling analysis Joint with Lucas Ambrozio, Reto Buzano and Alessandro Carlotto. Submitted 2018
  3. 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.
  4. 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.
  5. Index estimates for free boundary minimal hypersurfaces. Joint with Lucas Ambrozio and Alessandro Carlotto Math. Ann. 370 (2018), no. 3-4, 1063--1078.
  6. 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.
  7. 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.
  8. 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.
  9. 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.
  10. Compactness of minimal hypersurfaces with bounded index. J. Differential Geom. 106 (2017), no. 2, 317--339.
  11. 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.
  12. 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.
  13. 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.
  14. Higher integrability for solutions to a system of critical elliptic PDE. Methods. Appl. Anal., 21 (2014) No. 2, 221--240.
  15. 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.
  16. 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