arXiv research

The paper studies flow estimates on projective bundles.

Geodesic flow mixing on convex projective manifolds proven.

New flows on convex real projective structures on surfaces.

The paper preserves positivity along a flow over projective bundles.

Space of Zoll Finsler metrics on projective plane deformation retracts to round metric.

Generalizes surgery techniques for projectively Anosov flows.

Entropy study of geodesic flow on convex projective surfaces.

Classifies geodesic flows on projective plane with potential field.

New 3D shapes found without certain special flows.

Curve Shortening Flow preserves circularity for convex projections.

Geodesic flows on Kähler manifolds are quantum integrable when metrics are c-projectively equivalent.

In this paper, we study a family of curves on $S^2$ that defines a two-dimensional smooth projective plane. We use curve shortening flow to prove that any two-dimensional smooth projective plane can be smoothly deformed through a family of smooth projective planes into one which is isomorphic to the real projective pla…

Consider $E$ a holomorphic vector bundle over a projective manifold $X$ polarized by an ample line bundle $L$. Fix $k$ large enough, the holomorphic sections $H^0(E\otimes L^k)$ provide embeddings of $X$ in a Grassmanian space. We define the \textit{balancing flow for bundles} as a flow on the space of projectively equ…

We give the complete classification of regular projectively Anosov flows on closed three-dimensional manifolds. More precisely, we show that such a flow must be either an Anosov flow or decomposed into a finite union of $T^2 \times I$-models. We also apply our method to rigidity problems of some group actions.

We give complete classification of C^2-regular and non-degenerate projectively Anosov flows on three dimensional manifolds. More precisely, we prove that such a flow on a connected manifold must be either an Anosov flow or represented as a finite union of $T^2 \times [0,1]$-models.

The paper studies mean curvature flow of submanifolds in complex projective spaces.

The paper proves existence and behavior of Lagrangian tori in complex projective plane.

Classifies 2D complex superflows with finite symmetry groups.

New quantity helps map homotopy classes in complex spaces.

In this paper, we propose a method of studying the modified Kahler-Ricci flow on projective bundles and give the explicit equation from the view point of symplectic geometry.

Space curves with convex projections evolve smoothly until shrinking to a point.

Study on Gauduchon manifolds finds metrics for projectively flat bundles.

The paper classifies superflows in 2D and explores their properties in 3D.

Study of intersections in Hamiltonian orbits on cotangent bundles.

Study proves projective Anosov subgroups lead to mixing flows in specific spaces.

Complex projective space is unstable under Ricci flow, disproving conjectures.

We introduce cylindrical projections to simulate infinite-dimensional occupation flows of diffusions.

Study mean curvature flow of high codimension submanifolds in complex projective space.

Bi-contact surgery operations can be applied to Anosov flows.

Study classifies 3D superflows with icosahedral symmetry.

Proposes a Carbon Equivalence Principle for financial products to align incentives and drive sustainability.

Study of 2D metrics with one projective symmetry leading to superintegrable systems.

We study the Kähler-Ricci flow on a class of projective bundles $\mathbb{P}(\mathcal{O}_Σ\oplus L)$ over compact Kähler-Einstein manifold $Σ^n$. Assuming the initial Kähler metric $ω_0$ admits a U(1)-invariant momentum profile, we give a criterion, characterized by the triple $(Σ, L, [ω_0])$, under which the $\mathbb{P…

The study improves Perelman's theorems on Ricci flow.

Paper defines the payback period for nonconventional cash flows using axioms.

We extend the Besicovitch-Federer projection theorem to transversal families of mappings. As an application we show that on a certain class of Riemann surfaces with constant negative curvature and with boundary, there exist natural 2-dimensional measures invariant under the geodesic flow having 2-dimensional supports s…

PL-MCMC samples from normalizing flows' conditional distributions.

We consider the evolution by mean curvature flow of Lagrangian submanifolds of the complex projective space CP^n. We prove that, if the initial value satisfies a suitable pinching condition, then the flow exists for all times and the manifold converges to a totally geodesic submanifold. As a corollary, we obtain that a…

Establishes K"ahler-Ricci flow on log canonical varieties.

We show that the scalar curvature is uniformly bounded for the normalized Kahler-Ricci flow on a Kahler manifold with semi-ample canonical bundle. In particular, the normalized Kahler-Ricci flow has long time existence if and only if the scalar curvature is uniformly bounded, for Kahler surfaces, projective manifolds o…

We study the behaviour of the Kähler-Ricci flow on projective bundles. We show that if the initial metric is in a suitable Kähler class, then the fibers collapse in finite time and the metrics converge subsequentially in the Gromov-Hausdorff sense to a metric on the base.

New findings on geometric flows and equidistribution in Hilbert geometry.

We show that on any compact Riemann surface with variable negative curvature there exists a measure which is invariant and ergodic under the geodesic flow and whose projection to the base manifold is 2-dimensional and singular with respect to the 2-dimensional Lebesgue measure.

Let $S^{n}$ be the $n$-sphere of constant positive curvature. For $n \geq 2$, we will show that a measure on the unit tangent bundle of $S^{2n}$, which is even and invariant under the geodesic flow, is not uniquely determined by its projection to $S^{2n}$.

We study the local geometry of irreducible parabolic geometries admitting strongly essential flows; these are flows by local automorphisms with higher-order fixed points. We prove several new rigidity results, and recover some old ones for projective and conformal structures, which show that in many cases the existence…

Gradient flow preserves speed for integral Menger curvature curves.

Classifies surfaces of section for Seifert fibrations.

An investor is estimating net present value of a firm project and performs risk analysis. Usually it is created portfolio hierarchies and make comparison of variants of project based on these hierarchies. Then one finds that portfolio which corresponds to the particular needs of individual groups within the firm. We ha…