https://neckpinch.com/authors/shouvik-datta-choudhury/New arXiv papers by Shouvik Datta Choudhury, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2412.05281/arxiv:2412.05281Mon, 04 Nov 2024 00:00:00 GMTShouvik Datta Choudhury — This paper explores the evolution and monotonicity of geometric constants within the framework of extended Ricci flows, incorporating variable coupling parameters. Building on Hamiltons foundational Ricci flow and subsequent extensions by List (2008), we introduce modifications to the extended Ricci flow by varying parameters that affect the interaction between the metric and scalar fields. Specifically, we modify the coefficients in the evolution equations governing geometric constants, thereby introducing new degrees of freedom in the analysis. The primary contributions include deriving evolution formulas for the modified geometric constant lambda under the extended and normalized extended Ricci flows, and proving conditions under which monotonicity is maintained.Ricci flow https://neckpinch.com/papers/2411.03353/arxiv:2411.03353Mon, 04 Nov 2024 00:00:00 GMTShouvik Datta Choudhury — In this paper, we investigate the evolution of certain functionals involving higher powers of a scalar quantity F under Bernard List's extended Ricci flow on a compact Riemannian manifold. By deriving explicit expressions for the time derivative of integrals of the form ∫_M Fⁿ · ∂F/∂t dμ for various powers n, we explore the intricate interplay between geometric quantities and scalar functions without making any assumptions about the manifold, the scalar field Φ, or the function u.Ricci flow