17 citations · 37 across the 8 of their papers we have counts for
12 papers
curvature bounds for Type I Ricci flows
Panagiotis Gianniotis, Konstantinos Leskas
We show -bounds of the Riemann curvature tensor on a smooth closed -dimensional Ricci flow. To achieve this we introduce the notion of a neck of maximal symmetry, similar t…
Diameter bounds in 3d Type I Ricci flows
Panagiotis 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…
A -Hilbert functional in -geometry
Panagiotis Gianniotis, George Zacharopoulos
In this paper we introduce a new functional on the space of -structures which we call the -Hilbert functional. It is uniquely determined by a few basic principles inspire…
Splitting maps in Type I Ricci flows
Panagiotis 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 th…
Flows of -structures, II: Curvature, torsion, symbols, and functionals
Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis
We continue the investigation of general geometric flows of -structures initiated by the third author in "Flows of -structures, I." Specifically, we determine the possibl…
A gradient flow of isometric structures
Shubham Dwivedi, Panagiotis Gianniotis, Spiro Karigiannis
We study a flow of structures which induce the same Riemannian metric which is the negative gradient flow of an energy functional. We prove Shi-type estimates for the torsion…
Diameter and curvature control under mean curvature flow
Panagiotis Gianniotis, Robert Haslhofer
We prove that for the mean curvature flow of two-convex hypersurfaces the intrinsic diameter stays uniformly controlled as one approaches the first singular time. We also derive sh…
Regularity theory for Type I Ricci flows
Panagiotis Gianniotis
We consider Type I Ricci flows and obtain integral estimates for the curvature tensor valid up to, and including, the singular time. Our estimates partially extend to higher dimens…
Ricci flow from spaces with isolated conical singularities
Panagiotis Gianniotis, Felix Schulze
Let be a compact -dimensional Riemannian manifold with a finite number of singular points, where the metric is asymptotic to a non-negatively curved cone over $(\mathb…
The size of the singular set of a Type I Ricci flow
Panagiotis Gianniotis
In a singular Type I Ricci flow, we consider a stratification of the set where there is curvature blow-up, according to the number of the Euclidean factors split by the tangent flo…
Boundary estimates for the Ricci flow
Panagiotis Gianniotis
In this paper we consider the Ricci flow on manifolds with boundary with appropriate control on its mean curvature and conformal class. We obtain higher order estimates for the cur…
The Ricci flow on manifolds with boundary
Panagiotis Gianniotis
We study the short-time existence and regularity of solutions to a boundary value problem for the Ricci-DeTurck equation on a manifold with boundary. Using this, we prove the short…