Publications, preprints, unpublished docs

Mathematics Publications

  1. Boundary value problems for general first-order elliptic differential operators, (with C. Bär), J. Funct. Anal., 282(12):109445, 2022. [Arxiv version]. [Journal version]
  2. Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary, (with M. Nursultanov and J. Rowlett), Ann. Sc. Norm. Super. Pisa Cl. Sci., Vol. XXII, Issue 4, 2021. [Arxiv version]. [Journal version]
  3. Heat kernels and regularity for rough metrics on smooth manifolds, (with P. Bryan), Math. Nach., 293(12):2255–2270, 2020. [Arxiv version]. [Journal version]
  4. Functional calculus and harmonic analysis in geometry, SPJM, Special Section: An Homage to Manfredo P. do Carmo. (Online first). [Arxiv version] [Journal version].
  5. Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions, (with A. Rosén), Comms. PDE. Volume 44, Issue 12, 2019, Pages 1253-1284. [Arxiv version] [Journal Version].
  6. Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric, (with A. McIntosh and A. Rosén), Math. Ann. Volume 370, Issue 1–2, 2018, Pages 863–915. [Arxiv version] [Journal version].
  7. Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics , (with H. Saratchandran), J. Funct. Anal., Volume 273, Issue 12, 2017, Pages 3719-3758. [Arxiv version] [Journal version].
  8. Continuity of solutions to space-varying pointwise linear elliptic equations, Publ. Mat. 61 (2017), no. 1, 239-258. [Arxiv version] [Journal version].
  9. Geometric singularities and a flow tangent to the Ricci flow, (with S. Lakzian and M. Munn), Ann. Sc. Norm. Super. Pisa Cl. Sci. Vol. 17, No 2, 2017, pages. 763-804. [Arxiv version] [Journal version]
  10. Rough metrics on manifolds and quadratic estimates, Math. Z. 283 (2016), no. 3-4, 1245-1281. [Arxiv version] [Journal version].
  11. Self-adjointness of the Gaffney Laplacian on vector bundles, (with O. Milatovic), Math. Phys. Anal. Geom. 18 (2015), no. 1, Art. 17, 14 pp. [Arxiv version] [Journal version].
  12. The Kato square root problem on vector bundles with generalised bounded geometry, (with A. McIntosh), J. Geom. Anal. 26 (2016), no. 1, 428-462. [Arxiv version] [Journal version].
  13. Density problems on vector bundles and manifolds, Proc. Amer. Math. Soc. 142 (2014), no. 8, 2683-2695. [Arxiv version] [Journal version].
  14. Square roots of perturbed subelliptic operators on Lie groups, (with A.F.M ter Elst and A. McIntosh), Studia Math. 216 (2013), no. 3, 193-217. [Arxiv version] [Journal version].
  15. Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces, AMSI International Conference on Harmonic Analysis and Applications, Proc. Centre Math. Appl. Austral. Nat. Univ., vol. 45, Austral. Nat. Univ., Canberra, 2011, pp. 1-21. [Arxiv version] [Journal version].

Other publications

  1. ShapeRotator: An R tool for standardized rigid rotations of articulated three-dimensional structures with application for geometric morphometrics, Marta Vidal-García, Lashi Bandara, J. Scott Keogh, Ecology and Evolution. [Journal version].

Preprints

  1. The relative index theorem for general first-order elliptic operators, [Arxiv version]
  2. Realisations of elliptic operators on compact manifolds with boundary, (with M. Goffeng, H. Saratchandran), [Arxiv version]

Published books

  1. Real Harmonic Analysis, Lectures by Pascal Auscher with the assistance of Lashi Bandara, ANU Eview, 2012, [Online version].

Unpublished books

  1. Boundary value problems and index theory, Lashi Bandara, [BVPIT - 25012022], 2022.

Theses