12 citations · 69 across the 18 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…