12 citations · 69 across the 18 of their papers we have counts for
21 papers
A hitchhiker's guide to first-order elliptic boundary value problems
Christian Baer, Lashi Bandara
To empower the mathematical hitchhiker wishing to use operator methods in geometry and topology, we present this user's guide to first-order elliptic boundary value problems. Exist…
The space of rough Riemannian metrics
Lashi Bandara, Anisa Hassan
On a smooth connected manifold, we consider all possible locally elliptic and locally bounded measurable coefficient Riemannian metrics called rough Riemannian metrics. We equip th…
Geometric singularities and Hodge theory
Lashi Bandara, Georges Habib
We consider smooth vector bundles over smooth manifolds equipped with non-smooth geometric data. For nilpotent differential operators acting on these bundles, we show that the kern…
First-order elliptic boundary value problems on manifolds with non-compact boundary
Christian Baer, Lashi Bandara
We consider first-order elliptic differential operators acting on vector bundles over smooth manifolds with smooth boundary, which is permitted to be noncompact. Under very mild as…
The relative index theorem for general first-order elliptic operators
Lashi Bandara
The relative index theorem is proved for general first-order elliptic operators that are complete and coercive at infinity over measured manifolds. This extends the original result…
Realisations of elliptic operators on compact manifolds with boundary
Lashi Bandara, Magnus Goffeng, Hemanth Saratchandran
This paper investigates realisations of elliptic differential operators of general order on manifolds with boundary following the approach of Bär-Ballmann to first order elliptic o…
Boundary value problems for general first-order elliptic differential operators
Christian Baer, Lashi Bandara
We study boundary value problems for first-order elliptic differential operators on manifolds with compact boundary. The adapted boundary operator need not be selfadjoint and the b…
Eigenvalue asymptotics for weighted Laplace equations on rough Riemannian manifolds with boundary
Lashi Bandara, Medet Nursultanov, Julie Rowlett
Our topological setting is a smooth compact manifold of dimension two or higher with smooth boundary. Although this underlying topological structure is smooth, the Riemannian metri…
Functional calculus and harmonic analysis in geometry
Lashi Bandara
In this short survey article, we showcase a number of non-trivial geometric problems that have recently been resolved by marrying methods from functional calculus and real-variable…
Heat kernels and regularity for rough metrics on smooth manifolds
Lashi Bandara, Paul Bryan
We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Hölder contin…
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of local boundary conditions
Lashi Bandara, Andreas Rosén
On a smooth complete Riemannian spin manifold with smooth compact boundary, we demonstrate that the Atiyah-Singer Dirac operator in depen…
Essential self-adjointness of powers of first-order differential operators on non-compact manifolds with low-regularity metrics
Lashi Bandara, Hemanth Saratchandran
We consider first-order differential operators with locally bounded measurable coefficients on vector bundles with measurable coefficient metrics. Under a mild set of assumptions,…
Riesz continuity of the Atiyah-Singer Dirac operator under perturbations of the metric
Lashi Bandara, Alan McIntosh, Andreas Rosén
We prove that the Atiyah-Singer Dirac operator in depends Riesz continuously on perturbations of complete metrics $…
Continuity of solutions to space-varying pointwise linear elliptic equations
Lashi Bandara
We consider pointwise linear elliptic equations of the form on a smooth compact manifold where the operators are in divergence form with rea…
Geometric singularities and a flow tangent to the Ricci flow
Lashi Bandara, Sajjad Lakzian, Michael Munn
We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangen- tial to the Ricci flow almost-everywh…
Self-adjointness of the Gaffney Laplacian on vector bundles
Lashi Bandara, Ognjen Milatovic
We study the Gaffney Laplacian on a vector bundle equipped with a compatible metric and connection over a Riemannian manifold that is possibly geodesically incomplete. Under the hy…
Rough metrics on manifolds and quadratic estimates
Lashi Bandara
We study the persistence of quadratic estimates related to the Kato square root problem across a change of metric on smooth manifolds by defining a class of Riemannian-like metrics…
Density problems on vector bundles and manifolds
Lashi Bandara
We study some canonical differential operators on vector bundles over smooth, complete Riemannian manifolds. Under very general assumptions, we show that smooth, compactly supporte…
Square roots of perturbed subelliptic operators on Lie groups
Lashi Bandara, A. F. M. ter Elst, Alan McIntosh
We solve the Kato square root problem for bounded measurable perturbations of subelliptic operators on connected Lie groups. The subelliptic operators are divergence form operators…
The Kato square root problem on vector bundles with generalised bounded geometry
Lashi Bandara, Alan McIntosh
We consider smooth, complete Riemannian manifolds which are exponentially locally doubling. Under a uniform Ricci curvature bound and a uniform lower bound on injectivity radius, w…
Quadratic estimates for perturbed Dirac type operators on doubling measure metric spaces
Lashi Bandara
We consider perturbations of Dirac type operators on complete, connected metric spaces equipped with a doubling measure. Under a suitable set of assumptions, we prove quadratic est…