4 papers · 1 filter
Initial singularities of positive solutions of the Heat equation on Stratified Lie groups
Utsav Dewan
Let be a stratified Lie group. We estimate the Hausdorff dimension (with respect to the Carnot-Carathéodory metric) of the singular sets in , where…
Boundary exceptional sets for radial limits of superharmonic functions on non-positively curved Harmonic manifolds of purely exponential volume growth
Utsav Dewan
By classical Fatou type theorems in various setups, it is well-known that positive harmonic functions have non-tangential limit at almost every point on the boundary. In this paper…
Restricted mean value property on Riemannian manifolds
Kingshook Biswas, Utsav Dewan
A well studied classical problem is the harmonicity of functions satisfying the restricted mean-value property (RMVP). While this has so far been studied mainly for domains in $\ma…
Spectral projections and resolvent estimates on Damek-Ricci spaces and their applications
Mithun Bhowmik, Utsav Dewan
We prove boundedness of spectral projections and the resolvent of the Laplace-Beltrami operator on Damek-Ricci spaces with the explicit norms in terms of the spe…