Akashdeep Dey

activity

20192026

most citedA comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

19 citations · 34 across the 6 of their papers we have counts for

collaborators

7 papers

math.AP2026

Second order estimates on transition layers for the Allen-Cahn equation with homogeneous Neumann boundary conditions: Part I - Boundary-orthogonal transition layers

Akashdeep Dey, Wenkui Du, Davide Parise +1

We study stable solutions of the Allen-Cahn equation with homogeneous Neumann boundary condition on Riemannian manifolds with boundary in the regime where the transition layers mee…

math.DG2023

Existence of closed geodesics on certain non-compact Riemannian manifolds

Akashdeep Dey

Let $M$ be a complete Riemannian manifold. Suppose $M$ contains a bounded, concave, connected open set $U$ with $C^{0}$ boundary and $M ∖ U$ is connected. We assume that eithe…

math.DG2021★ 1 cited

The Allen-Cahn equation on the complete Riemannian manifolds of finite volume

Akashdeep Dey

The semi-linear, elliptic PDE $A C_{ε} (u) := - ε^{2} Δ u + W^{'} (u) = 0$ is called the Allen-Cahn equation. In this article we will prove the existence of finite energy soluti…

math.DG2020

A sub-additive inequality for the volume spectrum

Akashdeep Dey

Let $(M, g)$ be a closed Riemannian manifold and ${ω_{p}}_{p = 1}^{\infty}$ be the volume spectrum of $(M, g)$ . We will show that $ω_{k + m + 1} \leq ω_{k} + ω_{m} + W$ for all $k, m \geq 0$ , where $…

math.DG2020★ 19 cited

A comparison of the Almgren-Pitts and the Allen-Cahn min-max theory

Akashdeep Dey

Min-max theory for the Allen-Cahn equation was developed by Guaraco and Gaspar-Guaraco. They showed that the Allen-Cahn widths are greater than or equal to the Almgren-Pitts widths…

math.DG2019★ 7 cited

Existence of multiple closed CMC hypersurfaces with small mean curvature

Akashdeep Dey

Let $(M^{n + 1}, g)$ be a closed Riemannian manifold, $n + 1 \geq 3$ . We will prove that for all $m \in N$ , there exists $c^{*} (m) > 0$ , which depends on $g$ , such that if $0<c<c^…

math.DG2019★ 7 cited

Compactness of certain class of singular minimal hypersurfaces

Akashdeep Dey

Given a closed Riemannian manifold $(N^{n + 1}, g)$ , $n + 1 \geq 3$ we prove the compactness of the space of singular, minimal hypersurfaces in $N$ whose volumes are uniformly bounded f…