I study the behavior of solutions of a PDE over certain class of Riemannian manifold. Some of my works are based on gradient estimation techniques with curvature restrictions. I started my journey in research with Gradient estimation.
I also have a huge interest in Fundamental group, Growths of groups and volume of manifolds, Asymptotic geometry and Gromov-Hausdorff convergence. In future I would like to work in that field too.
Currently working on
Riemannian Manifold
Analysis of heat type equations on manifolds
Ricci flow
Gradient estimation
Willing to work on
Homology and Cohomology of manifolds
Gromov-Hausdorff convergence
Asymptotic geometry
References
S. K. Hui, A. Abolarinwa, and S. Bhattacharyya, ‘Liouville type theorem for weighted p-Laplacian and elliptic gradient estimate’, Sau Paulo Journal of Mathematical Sciences [ACCEPTED], 2024.
S. K. Hui, A. Abolarinwa, M. A. Khan, F. Mofarreh, A. Saha, and S. Bhattacharyya, ‘Li--Yau-Type Gradient Estimate along Geometric Flow’, Mathematics, vol. 11, no. 6, p. 1364, 2023.
S. K. Hui, A. Saha, and S. Bhattacharyya, ‘Hamilton and Souplet-Zhang type gradient estimate along geometric flow’, Filomat, vol. 37, no. 12, pp. 3939–3949, 2023.
Y. Li, S. Bhattacharyya, S. Azami, A. Saha, and S. K. Hui, ‘Harnack estimation for nonlinear, weighted, heat-type equation along geometric flow and applications’, Mathematics, vol. 11, no. 11, p. 2516, 2023.
S. K. Hui, A. Abolarinwa, and S. Bhattacharyya, “Li-yau, hamilton gradient and hessian estimates for nonlinear weighted parabolic equations and applications,” arXiv preprint arXiv:2303.13854, 2023.
S. K. Hui, A. Abolarinwa, and S. Bhattacharyya, ‘Gradient Estimations for Nonlinear Elliptic Equations on Weighted Riemannian Manifolds’, Lobachevskii Journal of Mathematics, vol. 44, pp. 1341–1349, 2023.
S. Bhattacharyya, S. Azami, and S. K. Hui, ‘Hamilton and Souplet--Zhang type estimations on semilinear parabolic system along geometric flow’, Indian Journal of Pure and Applied Mathematics, pp. 1–11, 2024.
Y. Li, S. Bhattacharyya, S. Azami, and S. K. Hui, ‘Li-Yau type estimation of a semilinear parabolic system along geometric flow’, Journal of Inequalities and Applications, vol. 2024, no. 1, p. 131, 2024.
S. Bhattacharyya, S. Ghosh, and S. K. Hui, ‘Bernstein type gradient estimation for weighted local heat equation’, Filomat, vol. 38, no. 17, pp. 6125–6134, 2024.