Publications, preprints, unpublished docs

Preprints

  1. Geometric singularities and Hodge theory, (with G. Habib). [Arxiv version]
  2. First-order elliptic boundary value problems on manifolds with non-compact boundary, (with C. Bär). [Arxiv version]

Mathematics Publications

  1. Realisations of elliptic operators on compact manifolds with boundary, (with M. Goffeng, H. Saratchandran), Advances in Mathematics, 420:108968, 2023. [Arxiv version] [Journal version]
  2. The relative index theorem for general first-order elliptic operators, Journal of Geometric Analysis, 33(10), August 2022. [Arxiv version] [Journal version]
  3. Boundary value problems for general first-order elliptic differential operators, (with C. Bär), Journal of Functional Analysis, 282(12):109445, 2022. [Arxiv version]. [Journal version]
  4. Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary, (with M. Nursultanov and J. Rowlett), Annali della Scuola Normale Superiore di Pisa Classe di Scienze, Vol. XXII, Issue 4, 2021. [Arxiv version]. [Journal version]
  5. Heat kernels and regularity for rough metrics on smooth manifolds, (with P. Bryan), Mathematische Nachrichten}, 293(12):2255--2270, 2020. [Arxiv version]. [Journal version]
  6. Functional calculus and harmonic analysis in geometry, São Paulo Journal of Mathematical Sciences, Special Section: An Homage to Manfredo P. do Carmo, 2019. [Arxiv version] [Journal version].
  7. Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions, (with A. Rosén), Communications in Partial Differential Equations, 44(12):1253--1284, 2019. [Arxiv version] [Journal Version].
  8. Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric, (with A. McIntosh and A. Rosén), Mathematische Annalen, 370(1-2):863--915, 2018. [Arxiv version] [Journal version].
  9. Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics , (with H. Saratchandran), Journal of Functional Analysis, 273(12):3719--3758, 2017. [Arxiv version] [Journal version].
  10. Continuity of solutions to space-varying pointwise linear elliptic equations, Publicacions Matemàtiques, 61(1):239--258, 2017. [Arxiv version] [Journal version].
  11. Geometric singularities and a flow tangent to the Ricci flow, (with S. Lakzian and M. Munn), Annali della Scuola Normale Superiore di Pisa Classe di Scienze, Serie V, 17(2):763--804, 2017. [Arxiv version] [Journal version]
  12. Rough metrics on manifolds and quadratic estimates, Mathematische Zeitschrift, 283(3-4):1245--1281, 2016. [Arxiv version] [Journal version].
  13. The Kato square root problem on vector bundles with generalised bounded geometry, (with A. McIntosh), Journal of Geometric Analysis, 26(1):428--462, 2016. [Arxiv version] [Journal version].
  14. Self-adjointness of the Gaffney Laplacian on vector bundles, (with O. Milatovic), Mathematical Physics, Analysis and Geometry, 18(1):Art. 17, 14, 2015. [Arxiv version] [Journal version].
  15. Density problems on vector bundles and manifolds, Proceedings of the American Mathematical Society},142( 8):2683--2695, 2014. [Arxiv version] [Journal version].
  16. Square roots of perturbed subelliptic operators on Lie groups, (with A.F.M ter Elst and A. McIntosh), Studia Mathematica, 216(3):193–217, 2013. [Arxiv version] [Journal version].
  17. Quadratic Estimates and perturbations of Dirac type operators on doubling measure metric spaces, AMSI International Conference on Harmonic Analysis and Applications, Proceedings of the Centre for Mathematics and its Applications, vol. 45, Australian National University, 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].

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

Other unpublished documents