@article{BaerBandara2022,
  author    = {B{\"a}r, Christian and Bandara, Lashi},
  title     = {Boundary value problems for general first-order elliptic differential operators},
  series = {Journal of functional analysis},
  volume    = {282},
  journal   = {Journal of functional analysis},
  number    = {12},
  publisher = {Elsevier},
  address   = {Amsterdam [u.a.]},
  issn      = {0022-1236},
  doi       = {10.1016/j.jfa.2022.109445},
  pages     = {69},
  year      = {2022},
  abstract  = {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 boundary condition need not be pseudo-local.We show the equivalence of various characterisations of elliptic boundary conditions and demonstrate how the boundary conditions traditionally considered in the literature fit in our framework. The regularity of the solutions up to the boundary is proven. We show that imposing elliptic boundary conditions yields a Fredholm operator if the manifold is compact. We provide examples which are conveniently treated by our methods.},
  language  = {en}
}
@article{BandaraBryan2020,
  author    = {Bandara, Lashi and Bryan, Paul},
  title     = {Heat kernels and regularity for rough metrics on smooth manifolds},
  series = {Mathematische Nachrichten},
  volume    = {293},
  journal   = {Mathematische Nachrichten},
  number    = {12},
  publisher = {Wiley-VCH},
  address   = {Weinheim},
  issn      = {0025-584X},
  doi       = {10.1002/mana.201800459},
  pages     = {2255 -- 2270},
  year      = {2020},
  abstract  = {We consider rough metrics on smooth manifolds and corresponding Laplacians induced by such metrics. We demonstrate that globally continuous heat kernels exist and are Holder continuous locally in space and time. This is done via local parabolic Harnack estimates for weak solutions of operators in divergence form with bounded measurable coefficients in weighted Sobolev spaces.},
  language  = {en}
}
@article{Bandara2021,
  author    = {Bandara, Lashi},
  title     = {Functional calculus and harmonic analysis in geometry},
  series = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo},
  volume    = {15},
  journal   = {S{\~a}o Paulo journal of mathematical sciences / Instituto de Matem{\´a}tica e Estat{\´i}stica da Universidade de S{\~a}o Paulo},
  number    = {1},
  publisher = {Springer},
  address   = {Cham},
  issn      = {1982-6907},
  doi       = {10.1007/s40863-019-00149-0},
  pages     = {20 -- 53},
  year      = {2021},
  abstract  = {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 harmonic analysis. We give a brief description of these methods as well as their interplay. This is a succinct survey that hopes to inspire geometers and analysts alike to study these methods so that they can be further developed to be potentially applied to a broader range of questions.},
  language  = {en}
}
@article{BandaraMcIntoshRosen2017,
  author    = {Bandara, Lashi and McIntosh, Alan and Rosen, Andreas},
  title     = {Riesz continuity of the Atiyah},
  series = {Mathematische Annalen},
  volume    = {370},
  journal   = {Mathematische Annalen},
  number    = {1-2},
  publisher = {Springer},
  address   = {Heidelberg},
  issn      = {0025-5831},
  doi       = {10.1007/s00208-017-1610-7},
  pages     = {863 -- 915},
  year      = {2017},
  abstract  = {We prove that the Atiyah-Singer Dirac operator in L2 depends Riesz continuously on L∞ perturbations of complete metrics g on a smooth manifold. The Lipschitz bound for the map depends on bounds on Ricci curvature and its first derivatives as well as a lower bound on injectivity radius. Our proof uses harmonic analysis techniques related to Calder{\´o}n's first commutator and the Kato square root problem. We also show perturbation results for more general functions of general Dirac-type operators on vector bundles.},
  language  = {en}
}
@article{VidalGarciaBandaraKeogh2018,
  author    = {Vidal-Garcia, Marta and Bandara, Lashi and Keogh, J. Scott},
  title     = {ShapeRotator},
  series = {Ecology and evolution},
  volume    = {8},
  journal   = {Ecology and evolution},
  number    = {9},
  publisher = {Wiley},
  address   = {Hoboken},
  issn      = {2045-7758},
  doi       = {10.1002/ece3.4018},
  pages     = {4669 -- 4675},
  year      = {2018},
  abstract  = {The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.},
  language  = {en}
}
@misc{Vidal‐GarciaBandaraKeogh2018,
  author    = {Vidal-Garc{\´i}a, Marta and Bandara, Lashi and Keogh, J. Scott},
  title     = {ShapeRotator},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {818},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-42632},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-426321},
  pages     = {9},
  year      = {2018},
  abstract  = {The quantification of complex morphological patterns typically involves comprehensive shape and size analyses, usually obtained by gathering morphological data from all the structures that capture the phenotypic diversity of an organism or object. Articulated structures are a critical component of overall phenotypic diversity, but data gathered from these structures are difficult to incorporate into modern analyses because of the complexities associated with jointly quantifying 3D shape in multiple structures. While there are existing methods for analyzing shape variation in articulated structures in two-dimensional (2D) space, these methods do not work in 3D, a rapidly growing area of capability and research. Here, we describe a simple geometric rigid rotation approach that removes the effect of random translation and rotation, enabling the morphological analysis of 3D articulated structures. Our method is based on Cartesian coordinates in 3D space, so it can be applied to any morphometric problem that also uses 3D coordinates (e.g., spherical harmonics). We demonstrate the method by applying it to a landmark-based dataset for analyzing shape variation using geometric morphometrics. We have developed an R tool (ShapeRotator) so that the method can be easily implemented in the commonly used R package geomorph and MorphoJ software. This method will be a valuable tool for 3D morphological analyses in articulated structures by allowing an exhaustive examination of shape and size diversity.},
  language  = {en}
}