16 citations · 33 across the 21 of their papers we have counts for
25 papers
Ricci curvature of semigroup walks on graphs and generator representations
Sajjad Lakzian
We present an operator-theoretic framework for the Ollivier--Ricci curvature of (one-parameter families of) random walks generated by positive semigroups on graphs. On a metrically…
Positive mass and rigidity for asymptotically flat tangent bundles
Sajjad Lakzian
Let be an asymptotically flat manifold such that its tangent bundle is diffeomorphically asymptotically Euclidean. We prove a positive mass theorem and a positive mass…
On classification of Finslerian spaces with nontrivial concircular transformations
Zohreh Fathi, Sajjad Lakzian
We prove that in a non-trivial conformal circle-preserving transformation (CPT for short), on a (forward or backward) complete Finslerian manifold , the conformal fac…
On the rigidity of Finslerian conformal circle-preserving transformations
Zohreh Fathi, Sajjad Lakzian
We prove that if a forward or backward complete Berwaldian or reversible Finslerian manifold admits a non-trivial (non-homothety) conformal concircular transformation ({\bf…
The rigidity of conformal circle-preserving transformations on Berwaldian manifolds
Zohreh Fathi, Sajjad Lakzian
We prove that a complete Berwaldian manifold admitting a nontrivial conformal circle preserving transformation (\cpt for short) must be Riemannian, provided that…
On weak formulations of (super) Ricci flows
Sajjad Lakzian
We present two characterizations of smooth compact Ricci flow solutions solely in terms of metrics and measures (one of them only works under positive scalar curvature along the fl…
A generalization of the inverse mapping theorem in infinite dimensions
Sajjad Lakzian
We present a generalization of the inverse mapping theorem, where variations of a weaker non-expansiveness property (referred to as property ) replace the key $\mathsf{C}^…
On Rigidity of ALE vector bundles
Fatemeh Asadi, Zohreh Fathi, Sajjad Lakzian
We discuss topological rigidity of vector bundles with asymptotically conical (AC) total spaces of rank greater than 1 with a sufficiently connected link; our focus will mainly be…
Discrete Ollivier-Ricci curvature
Zohreh Fathi, Sajjad Lakzian
We analyze both continuous and discrete-time Ollivier-Ricci curvatures of locally-finite weighted graphs $\G$ equipped with a given distance "$\dist$" (w.r.t. which $\G$ is metrica…
The rigidity of sharp spectral gap in nonnegatively curved spaces
Christian Ketterer, Yu Kitabeppu, Sajjad Lakzian
We extend the celebrated rigidity of the sharp first spectral gap under to compact infinitesimally Hilbertian spaces with non-negative (weak, also called synthetic) Ricci…
On Weak Super Ricci Flow through Neckpinch
Sajjad Lakzian, Michael Munn
In this article, we study the Ricci flow neckpinch in the context of metric measure spaces. We introduce the notion of a Ricci flow metric measure spacetime and of a weak (refined)…
Bakry-Émery Ricci curvature of doubly warped product of weighted spaces
Zohreh Fathi, Sajjad Lakzian
We introduce a notion of doubly warped product of weighted graphs that is consistent with the doubly warped product in the Riemannian setting. We establish various discrete Bakry-É…
Bubble tree convergence for harmonic maps into compact locally CAT(1) spaces
Christine Breiner, Sajjad Lakzian
We determine bubble tree convergence for a sequence of harmonic maps, with uniform energy bounds, from a compact Riemann surface into a compact locally CAT(1) space. In particular,…
Global Poincaré inequality on Graphs via Conical Curvature-Dimension Conditions
Sajjad Lakzian, Zachary McGuirk
We introduce and study the conical curvature-dimension condition, , for graphs. We show that provides necessary and sufficient conditions for the underlying gr…
Characterization of equality in Zhong-Yang type (sharp) spectral gap estimates for metric measure spaces
Sajjad Lakzian
We prove that a compact (or equivalently ) metric measure space, , with $\diam X \le d$ and its first (nonzero) eigenvalue of the Lapl…
Geometric singularities and a flow tangent to the Ricci flow
Lashi Bandara, Sajjad Lakzian, Michael Munn
We consider a geometric flow introduced by Gigli and Mantegazza which, in the case of smooth compact manifolds with smooth metrics, is tangen- tial to the Ricci flow almost-everywh…
Characterization of Low Dimensional spaces
Yu Kitabeppu, Sajjad Lakzian
In this paper, we give the characterization of metric measure spaces that satisfy synthetic lower Riemannian Ricci curvature bounds (so called spaces) with \emph{non-e…
On Closed Geodesics in Non-negatively Curved Finsler Structures with Large Volume Growth
Sajjad Lakzian
We prove that a reversible Berwaldian Finsler structure with base-independent non-negative radial flag curvature and large volume growth does not have any closed…
Non-branching RCD(0,N) Geodesic Spaces with Small Linear Diameter Growth Have Finitely Generated Fundamental Groups
Yu Kitabeppu, Sajjad Lakzian
In this paper, we generalize the finite generation result of Sormani to non-branching geodesic spaces (and in particular, Alexandrov spaces) with full support measures.…
On the Size of a Ricci Flow Neckpinch via Optimal Transport
Sajjad Lakzian, Michael Munn
In this paper we apply techniques from optimal transport to study the neckpinch examples of Angenent-Knopf which arise through the Ricci flow on . In particular,…
Differential Harnack Estimates for heat Equation under Finsler-Ricci Flow
Sajjad Lakzian
In this paper we prove first order differential Harnack estimates for positive solutions of the heat equation (in the sense of distributions) under closed Finsler-Ricci flows. We a…
Super Ricci flow for disjoint unions
Sajjad Lakzian, Michael Munn
In this paper we consider compact, Riemannian manifolds each equipped with a one-parameter family of metrics satisfying the Ricci flow equation. Motivat…
Continuity of Ricci Flow Through Neck Pinch Singularities
Sajjad Lakzian
In this article, we consider the Angenent-Caputo-Knopf's Ricci Flow through neckpinch singularities. We will explain how one can see the A-C-K's Ricci flow through a neckpinch sing…
Diameter Controls and Smooth Convergence away from Singular Sets
Sajjad Lakzian
We prove that if a family of metrics, , on a compact Riemannian manifold, , have a uniform lower Ricci curvature bound and converge to smoothly away from a sin…