6 papers
On improved Hardy-type inequalities in Log-Weighted Sobolev Spaces
Sourav Ghosh
We prove sharp Hardy-type inequalities in Log-weighted Sobolev spaces. Due to the non-attainability of the sharp constant, we improve these inequalities by adding suitable remainde…
Uniqueness of tangent flows in free boundary flow
Sourav Ghosh
We prove uniqueness of tangent flows for mean curvature flow with free boundary at singularities modeled on half-cylindrical self-shrinkers. More precisely, if a tangent flow is of…
Leray-Trudinger Type Exponential Integrability in Log-Weighted Sobolev Spaces
Adimurthi, Sourav Ghosh, Arka Mallick
In this article, we conduct a comprehensive study of weighted Sobolev spaces with logarithmic weights, orginially introduced by Calanchi and Ruf to analyze the sharp exponential in…
Decay order bound for mean curvature flow near compact singularities
Sourav Ghosh
We consider the rescaled flow associated with a mean curvature flow that develops a compact singularity of multiplicity one. We prove that the ``decay order'' of such a rescaled fl…
Cylindrical tangent flows in mean curvature flow
Sourav Ghosh
The only non-compact linearly stable singularity models for mean curvature flow are cylindrical, as shown by Colding-Minicozzi. The uniqueness of blowups at singularities modeled o…
Lagrangian mean curvature flow of surfaces with mean curvature bound
Sourav Ghosh
Let be a zero Maslov Lagrangian mean curvature flow in We show that if the mean curvature stays uniformly bounded along the flow, then the tangent flow at a s…