https://neckpinch.com/authors/chandan-kumar-mondal/New arXiv papers by Chandan Kumar Mondal, from Neckpinch Wed, 04 Nov 2026 08:05:15 GMT https://neckpinch.com/papers/2611.03823/arxiv:2611.03823Mon, 02 Nov 2026 00:00:00 GMTChandan Kumar Mondal — We study the behaviour of the conjugate radius under the Ricci flow on complete noncompact manifolds. We show that if (Mⁿ,g(t))_(t∈[0,T]) is a complete Ricci flow with nonnegative scalar curvature at t=0, the initial metric is parabolic and not Ricci-flat, and the Einstein tensor Ric-1/2 Rg is bounded above, then parabolicity is preserved along the flow and the conjugate radius of g(t) is finite for every t∈(0,T]. As an application, we prove that a complete noncompact gradient shrinking Ricci soliton whose volume growth is subquadratic, in the sense that liminf_(r→∞)Vol(B(p,r))/r²=0, has finite conjugate radius.Ricci flowRicci solitonsRicci-flat & Calabi–YauScalar curvatureBoundaries & non-compact