Sheela Verma

activity

20182026

most citedAn upper bound for the first nonzero Neumann eigenvalue

4 citations · 4 across the 14 of their papers we have counts for

collaborators

16 papers

math.SP2026

On domain monotonicity of Steklov eigenvalues

Sagar Basak, Sheela Verma

In this article, we prove a variant of domain monotonicity property for the Steklov eigenvalues of the Laplacian on strictly star-shaped bounded domains contained in $R^{n}$ …

math.AP2026

Sharp bounds and geometric properties of the first non trivial Steklov Neumann Eigenvalue

Sagar Basak, Gloria Paoli, Rossano Sannipoli +1

In this article, we study the mixed Steklov--Neumann eigenvalue problem on doubly connected domains. First, we show that among all doubly connected domains in $R^{n}$ of the…

math.AP2026

On Eigenvalues of Logarithmic Potential Operator in the Hyperbolic Space

Jiya Rose Johnson, Sheela Verma

Let $Ω$ be a bounded open set in the Poincaré hyperbolic disk, $D$ . In this article, we consider the hyperbolic logarithmic potential operator $\mathcal{L}_h : L^2(Ω) \to…

math.SP2025

Sharp bounds and monotonicity results for Neumann eigenvalues on graphs

Ashmita Singh, Sheela Verma

In this article, we study sharp bounds for the Neumann eigenvalues of the Laplace operator on graphs. We first establish both lower and upper bounds for the second Neumann eigenval…

math.SP2024

Bounds for higher Steklov and mixed Steklov Neumann eigenvalues on domains with holes

Sagar Basak, Sheela Verma

In this article, we study Steklov eigenvalues and mixed Steklov Neumann eigenvalues on a smooth bounded domain in $R^{n}$ , $n \geq 2$ , having a spherical hole. We focus on…

math.SP2023

Sharp bounds for higher Steklov-Dirichlet eigenvalues on domains with spherical holes

Sagar Basak, Anisa Chorwadwala, Sheela Verma

We consider mixed Steklov-Dirichlet eigenvalue problem on smooth bounded domains in Riemannian manifolds. Under certain symmetry assumptions on multiconnected domains in $\mathbb{R…

math.DG2023

An isoperimetric inequality for the harmonic mean of Steklov eigenvalues in rank one symmetric spaces

Hemangi Madhusudan Shah, Sheela Verma

In this note, an isoperimetric inequality for the harmonic mean of lower order Steklov eigenvalues is proved on bounded domains in noncompact rank- $1$ symmetric spaces. This work e…

math.AP2022

Reverse Faber-Krahn inequality for the $p$ -Laplacian in Hyperbolic space

Mrityunjoy Ghosh, Sheela Verma

In this paper, we study the shape optimization problem for the first eigenvalue of the $p$ -Laplace operator with the mixed Neumann-Dirichlet boundary conditions on multiply-connect…

math.DG2022

Szegö-Weinberger type inequalities for symmetric domains in simply connected space forms

T. V. Anoop, Sheela Verma

We consider the Neumann eigenvalue problem for Laplacian on a bounded multi-connected domain contained in simply connected space forms. Under certain symmetry assumptions on the do…

math.DG2020

Sharp Steklov upper bound for submanifolds of revolution

Bruno Colbois, Sheela Verma

In this note, we find a sharp upper bound for the Steklov spectrum on a submanifold of revolution in Euclidean space with one boundary component.

math.DG2020

An isoperimetric inequality for harmonic mean of Steklov eigenvalues in Hyperbolic space

Sheela Verma

In this article, we prove an isoperimetric inequality for the harmonic mean of the first $(n - 1)$ nonzero Steklov eigenvalues on bounded domains in $n$ -dimensional Hyperbolic space.…

math.DG2019★ 4 cited

An upper bound for the first nonzero Neumann eigenvalue

Sheela Verma

Let $M$ denote a complete, simply connected Riemannian manifold with sectional curvature $K_{M} \leq k$ and Ricci curvature $Ric_{M} \geq (n - 1) K$ ,…

math.DG2019

Some sharp bounds for Steklov eigenvalues

Sheela Verma, G. Santhanam

This work is an extension of a result given by Kuttler and Sigillito (SIAM Rev $10$ : $368 - 370$ , $1968$ ) on a star-shaped bounded domain in $R^{2}$ . Let $Ω$ be a star-shaped b…

math.AP2018

Upper bound for the first non-zero eigenvalue of the $p$ -Laplacian

Sheela Verma

Let $M$ be a closed hypersurface in $R^{n}$ and $Ω$ be a bounded domain such that $M = \partial Ω$ . In this article, we obtain an upper bound for the first non-zero eigenval…

math.DG2018

On Eigenvalue Problems Related to the Laplacian in a Class of Doubly Connected Domains

Sheela Verma

We consider two eigenvalue problems for Laplacian on some specific doubly connected domain. In particular, we study the following two eigenvalue problems. Let $B_{1}$ be an open ball…

math.DG2018

Bounds for the first non-zero Steklov eigenvalue

Sheela Verma

Let $Ω$ be a star-shaped bounded domain in $(S^{n}, d s^{2})$ with smooth boundary. In this article, we give a sharp lower bound for the first non-zero eigenvalue of the St…

On domain monotonicity of Steklov eigenvalues

Sharp bounds and geometric properties of the first non trivial Steklov Neumann Eigenvalue

On Eigenvalues of Logarithmic Potential Operator in the Hyperbolic Space

Sharp bounds and monotonicity results for Neumann eigenvalues on graphs

Bounds for higher Steklov and mixed Steklov Neumann eigenvalues on domains with holes

Sharp bounds for higher Steklov-Dirichlet eigenvalues on domains with spherical holes

An isoperimetric inequality for the harmonic mean of Steklov eigenvalues in rank one symmetric spaces

Reverse Faber-Krahn inequality for the p-Laplacian in Hyperbolic space

Szegö-Weinberger type inequalities for symmetric domains in simply connected space forms

Sharp Steklov upper bound for submanifolds of revolution

An isoperimetric inequality for harmonic mean of Steklov eigenvalues in Hyperbolic space

An upper bound for the first nonzero Neumann eigenvalue

Some sharp bounds for Steklov eigenvalues

Upper bound for the first non-zero eigenvalue of the p-Laplacian

On Eigenvalue Problems Related to the Laplacian in a Class of Doubly Connected Domains

Bounds for the first non-zero Steklov eigenvalue

Reverse Faber-Krahn inequality for the $p$ -Laplacian in Hyperbolic space

Upper bound for the first non-zero eigenvalue of the $p$ -Laplacian