https://neckpinch.com/authors/shubham-dwivedi/New arXiv papers by Shubham Dwivedi, from Neckpinch Tue, 03 Nov 2026 08:41:12 GMT https://neckpinch.com/papers/2611.02062/arxiv:2611.02062Sun, 01 Nov 2026 00:00:00 GMTVicente Cortés, Shubham Dwivedi, Lorenz Jetter — We prove that on a connected, simply-connected nilpotent Lie group, the notions of left-invariant generalized Ricci soliton, semi-algebraic and algebraic generalized Ricci soliton coincide. Moreover, every such soliton has harmonic torsion. We classify all algebraic solitons with positive definite metric on the five-dimensional Heisenberg algebra, the four-dimensional oscillator algebra and the four-dimensional split-oscillator algebra up to automorphisms and rescalings. We find that there is only a finite number of algebraic solitons, all of which have harmonic torsion.Generalized & G₂ flowsRicci solitons4-manifoldsHomogeneous spaces https://neckpinch.com/papers/2609.15880/arxiv:2609.15880Mon, 14 Sep 2026 00:00:00 GMTShubham Dwivedi — We study an adapted Ricci flow of connections with metric torsion on surfaces with positive Euler characteristic. We first prove that there do not exist any nontrivial solitons of the flow on the 2-sphere thus confirming a conjecture of Branding–Kröncke (J. Geom. Anal. 27.3 (2017), arXiv:1606.09121). We give an explicit family of torsion data for which the corresponding global solutions fail to converge on S². Nevertheless, we provide several sufficient conditions for the convergence of the flow to a stationary point. We first prove that the normalized adapted Ricci flow always converges on ℝP}², which completely answers a question in the paper of Branding and Kröncke. Using this, we deduce that the flow converges on S² whenever the initial metric and the torsion one-form are antipodally symmetric. We also prove a Łojasiewicz–Simon gradient inequality for the flow and use it to prove convergence to a stationary point provided the solution is close to an arbitrary stationary point.Ricci flowSurfacesLong-time existence & convergence https://neckpinch.com/papers/2601.05210/arxiv:2601.05210Thu, 08 Jan 2026 00:00:00 GMTShubham Dwivedi — We introduce and study a new general flow of G₂-structures which we call the Ricci-harmonic flow of G₂-structures. The flow is the coupling of the Ricci flow of underlying metrics and the isometric flow of G₂-structures, but we also provide explicit lower order in the torsion terms. The lower order terms and the flow are obtained by analyzing the second order term in the Taylor series expansion of G₂-structures in normal coordinates. As such, the Ricci-harmonic flow described in the paper can be interpreted as the "heat equation" for G₂-structures. The lower order terms allow us to prove that the stationary points of the Ricci-harmonic flow are exactly torsion-free G₂-structures on compact manifolds. We study various analytic and geometric properties of the flow. We show that the flow has short-time existence and uniqueness on compact manifolds starting with an arbitrary G₂-structure and prove global Shi-type estimates. We also prove a modified local Shi-type estimates for the flow which assume bounds on the initial derivatives of the Riemann curvature tensor and the torsion but give uniform bounds on these quantities for all times. We prove a compactness theorem for the solutions of the flow and use it to prove that the Ricci-harmonic flow exists as long as the velocity of the flow remains bounded. We also study Ricci-harmonic solitons where we prove that there are no compact expanding solitons and the only steady solitons are torsion-free. We derive an analog of Hamilton's identity for gradient Ricci-harmonic solitons and prove some integral identities for the solitons. Finally, we prove a version of the Taylor series expansion for Spin(7)-structures and use it to derive the Ricci-harmonic flow of Spin(7)-structures.Ricci flowRicci solitonsLimit spaces & RCDStability & uniquenessHarmonic maps & DeTurck trick