4 papers · 1 filter
Bol's type inequality for singular metrics and its application to prescribing -curvature problems
Mrityunjoy Ghosh, Ali Hyder
In this article, we study higher-order Bol's inequality for radial normal solutions to a singular Liouville equation. By applying these inequalities along with compactness argument…
Isoperimetric inequality with zero magnetic field in doubly connected domains
Mrityunjoy Ghosh, Ayman Kachmar
We investigate how the lowest eigenvalue of a magnetic Laplacian depends on the geometry of a planar domain with a disk shaped hole, where the magnetic field is generated by a sing…
Isoperimetric inequalities for the fractional composite membrane problem
Mrityunjoy Ghosh
In this article, we investigate some isoperimetric-type inequalities related to the first eigenvalue of the fractional composite membrane problem. First, we establish an analogue o…
On the optimization of the first weighted eigenvalue of the fractional Laplacian
Mrityunjoy Ghosh
In this article, we consider the minimization problem for the first eigenvalue of the fractional Laplacian with respect to the weight functions lying in the rearrangement classes o…