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Anjali Shriwastawa

Publications and source records attributed to Anjali Shriwastawa.

7 recordsLinked to original sources
arXiv2026

Finite Volume Einstein Finsler Warped Product Manifolds of Non-positive or Non-negative Scalar Curvature

The notion of warped product plays an important role in Riemannian geometry moreover in geodesic metric spaces. The warped product was first introduced by Bishop and O'Neill to study Riemannian manifolds of negative curvature.Warped products have been mainly used to construct new examples of Riemannian manifolds with prescribed curvature conditions. This construction can be extended for Finslerian metrics with some minor restrictions. This is motivated by Asanov's papers, where some models of relativity theory are described through the warped product of Finsler metrics. These metrics are in the form of $(α,β)$-metrics, which are the generalization of the Randers metrics; which are being asymmetric Finsler metrics in four-dimensional space-time. The product was later extended to the warped product case of Finsler manifolds by the work of Kozma, Peter and Verge.

math.DG↗
arXiv2024

Bilinear Hardy inequalities on metric measure spaces

In this paper, we discuss the Hardy inequality with bilinear operators on general metric measure spaces. We give the characterization of weights for the bilinear Hardy inequality to hold on general metric measure spaces having polar decompositions. We also provide several examples of the results, finding conditions on the weights for integral Hardy inequalities on homogeneous Lie groups, as well as on hyperbolic spaces and more generally on Cartan-Hadamard manifolds.

math.FA↗
arXiv2024

Sharp upper bound for anisotropic Rényi entropy and Heisenberg uncertainty principle

In this paper, we prove the anisotropic Shannon inequality for the Renyi entropy with the best constant on Folland-Stein homogeneous Lie groups. As a consequence, we also prove the optimal Shannon inequality in the same setting. Using a logarithmic Sobolev inequality in the setting of stratified groups, we prove a Heisenberg-type uncertainty principle in the latter setting.

math.FA↗
arXiv2023

Anisotropic weighted Levin-Cochran-Lee type inequalities on homogeneous Lie groups

In this paper, we first prove the weighted Levin-Cochran-Lee type inequalities on homogeneous Lie groups for arbitrary weights, quasi-norms, and $L^p$-and $L^q$-norms. Then, we derive a sharp weighted inequality involving specific weights given in the form of quasi-balls in homogeneous Lie groups. Finally, we also calculate the sharp constants for the aforementioned inequalities.

math.CA↗
arXiv2022

Hardy inequalities on metric measure spaces, IV: The case $p=1$

In this paper, we investigate the two-weight Hardy inequalities on metric measure space possessing polar decompositions for the case $p=1$ and $1 \leq q <\infty.$ This result complements the Hardy inequalities obtained in \cite{RV} in the case $1< p\le q<\infty.$ The case $p=1$ requires a different argument and does not follow as the limit of known inequalities for $p>1.$ As a byproduct, we also obtain the best constant in the established inequality. We give examples obtaining new weighted Hardy inequalities on homogeneous Lie groups, on hyperbolic spaces and on Cartan-Hadamard manifolds for the case $p=1$ and $1\le q<\infty.$

math.CA↗
arXiv2022

A note on best constants for Weighted Integral Hardy inequalities on homogeneous groups

The main aim of this note is to prove sharp weighted integral Hardy inequality and conjugate integral Hardy inequality on homogeneous Lie groups with any quasi-norm for the range $1<p\leq q<\infty.$ We also calculate the precise value of sharp constants in respective inequalities, improving the result of $[19]$ in the case of homogeneous groups.

math.AP↗