https://neckpinch.com/authors/panagiotis-gianniotis/New arXiv papers by Panagiotis Gianniotis, from Neckpinch Tue, 03 Nov 2026 07:15:30 GMT https://arxiv.org/abs/2510.22660arxiv:2510.22660Sun, 26 Oct 2025 00:00:00 GMTPanagiotis Gianniotis, Konstantinos Leskas — We show L¹-bounds of the Riemann curvature tensor on a smooth closed n-dimensional Ricci flow. To achieve this we introduce the notion of a neck of maximal symmetry, similar to the one in Cheeger-Jiang-Naber and Jiang-Naber and establish a decomposition result by balls with uniform curvature bounds that satisfy an appropriate (n-2)-content estimate.Ricci flowSingularities https://arxiv.org/abs/2510.14019arxiv:2510.14019Wed, 15 Oct 2025 00:00:00 GMTPanagiotis Gianniotis — We prove that a three dimensional compact Ricci flow that encounters a Type I singularity has uniformly bounded diameter up to the singular time, thus giving an affirmative answer - for Type I singularities - to a conjecture of Perelman. To achieve this, we introduce a concept of a neck-region for a Ricci flow, analogous to the neck-regions introduced by Jiang-Naber and Cheeger-Jiang-Naber, in the study of Ricci limit spaces. We then prove that the associated packing measure is, in a certain sense, Ahlfors regular, a result that holds in any dimension.Ricci flowSingularities3-manifoldsLimit spaces & RCD https://arxiv.org/abs/2505.06872arxiv:2505.06872Sun, 11 May 2025 00:00:00 GMTPanagiotis Gianniotis, George Zacharopoulos — In this paper we introduce a new functional on the space of G₂-structures which we call the G₂-Hilbert functional. It is uniquely determined by a few basic principles inspired by the Einstein-Hilbert functional in Riemannian Geometry, and it has similar variational behaviour with it. For instance, torsion-free and nearly G₂-structures are saddle critical points of the volume-normalized G₂-Hilbert functional. This allows us to uniquely distinguish two new flows of G₂-structures, which can be considered as analogues of the Ricci flow in G₂-geometry.Ricci flowGeneralized & G₂ flows https://arxiv.org/abs/2403.20070arxiv:2403.20070Fri, 29 Mar 2024 00:00:00 GMTPanagiotis Gianniotis — We study the existence and small scale behaviour of almost splitting maps along a Ricci flow satisfying Type I curvature bounds. These are special solutions of the heat equation that serve as parabolic analogues of harmonic almost splitting maps, which have proven to be an indespensable tool in the study of the structure of the singular set of non-collapsed Ricci limit spaces. In this paper, motivated by the recent work of Cheeger-Jiang-Naber in the Ricci limit setting, we construct sharp splitting maps on Ricci flows that are almost selfsimilar, and then investigate their small scale behaviour. We show that, modulo linear transformations, an almost splitting map at a large scale remains a splitting map even at smaller scales, provided that the Ricci flow remains sufficiently self-similar. Allowing these linear transformations means that a priori an almost splitting map might degenerate at small scales. However, we show that under an additional summability hypothesis such degeneration doesn't occur.Ricci flowSingularities(Non)collapsingLimit spaces & RCD