arXiv research

In this paper, we introduce the weighted mixed (sectional, Ricci and scalar) curvature of a foliated (and almost-product) Riemannian manifold $(M,g)$ equipped with a vector field $X$. We define several functions ($q$th Ricci type curvatures), which "interpolate" between the weighed sectional and Ricci curvatures. The n…

Paper develops methods for estimating gradients of Finslerian Schrödinger equations.

Researchers estimate gradients of solutions to a Finslerian Allen-Cahn equation.

Researchers prove constant solutions for a specific Finslerian equation.

Proves almost flat manifolds with mixed curvature bounds.

Study on Kähler manifolds with non-positive mixed curvature and its implications.

For all complex dimensions n>=2, we construct complete Kaehler manifolds of bounded curvature and non-negative Ricci curvature whose Kaehler--Ricci evolutions immediately acquire Ricci curvature of mixed sign.

The paper explores mixed curvature for Hermitian manifolds and its implications.

The paper studies weighted Ricci curvatures and characterizes Randers metrics.

Study on stable minimal hypersurfaces under Ricci curvature constraints.

The paper studies solutions to a nonlinear equation on Finsler manifolds with gradient estimates and Harnack inequalities.

In this paper, we introduce the weighted projective Ricci curvature as an extension of projective Ricci curvature introduced by Z. Shen. We characterize the class of Randers metrics of weighted projective Ricci flat curvature. We find the necessary and sufficient condition under which a Kropina metric has weighted proj…

We establish new obstruction results to the existence of Riemannian metrics on tori satisfying mixed bounds on both their sectional and Ricci curvatures. More precisely, from Lohkamp's theorem, every torus of dimension at least three admits Riemannian metrics with negative Ricci curvature. We show that the sectional cu…

The paper proves conditions for projectivity and rational connectedness of complex manifolds with quasi-positive mixed curvature.

Study on mixed Killing vector fields on Cigar Ricci-Bourguignon solitons.

Study improves Poisson equation solutions on various manifolds.

Introduces new curvature concept for Kähler manifolds.

Proves Ricci flow extensibility with integral norms.

This paper is devoted to the study of the evolution of positively curved metrics on the Wallach spaces $SU(3)/T_{\max}$, $Sp(3)/Sp(1)\times Sp(1)\times Sp(1)$, and $F_4/Spin(8)$. We prove that for all Wallach spaces, the normalized Ricci flow evolves all generic invariant Riemannian metrics with positive sectional curv…

New method calculates Ricci curvature from distances between weighted volumes.

Study of Ricci flow on trees, focusing on edge weights and curvatures.

Study geometric properties and physical applications of mixed quasi-Einstein spacetime.

We study Riemannian manifolds with boundary under a lower weighted Ricci curvature bound. We consider a curvature condition in which the weighted Ricci curvature is bounded from below by the density function. Under the curvature condition, and a suitable condition for the weighted mean curvature for the boundary, we ob…

The study examines constant weighted mean curvature hypersurfaces in shrinking Ricci solitons.

The paper introduces curvature-based clustering algorithms for graph analysis.

We consider a problem of prescribing the partial Ricci curvature on a locally conformally flat manifold $(M^n, g)$ endowed with the complementary orthogonal distributions $D_1$ and $D_2$. We provide conditions for symmetric $(0,2)$-tensors $T$ of a simple form (defined on $M$) to admit metrics $\tilde g$, conformal to …

Study geometric and topological properties of Finsler manifolds with weighted Ricci curvature bounds.

Study on Kähler manifolds with non-negative mixed curvature, proving splitting and structure theorems.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

A flow of metrics, $g_t$, on a manifold is a solution of a differential equation $\dt g = S(g)$, where a geometric functional $S(g)$ is a symmetric $(0,2)$-tensor usually related to some kind of curvature. The mixed sectional curvature of a foliated manifold regulates the deviation of leaves along the leaf geodesics. W…

Proves equivalence of two types of Ricci curvature bounds.

The paper studies constant $k$th-mixed curvature on Hermitian manifolds and finds self-duality and Kähler conditions.

Paper extends Aronson-Bénilan estimates for porous medium equations on manifolds with negative curvature.

Study preserves metrics with positive Bakry-Émry Ricci curvature via surgery.

Study improves understanding of Ricci curvature in manifolds.

Paper proves new theorems about curvature in weighted manifolds.

Study compares manifolds with boundary under weighted Ricci curvature bounds.

Sharp isoperimetric inequality on Finsler manifolds with non-negative Ricci curvature.

Ricci-Filtration enhances retrieval-augmented generation rerankers for query-answer tasks by using discrete Ricci flow on graphs.

Study complete manifolds with weighted Poincaré inequality and Ricci curvature bounds.

The study establishes inequalities on Finsler manifolds with weighted Ricci curvature.

Paper investigates rigidity phenomena for weighted Ricci curvature bounds with Laplacian comparison theorem.

The paper studies Ricci flow on graphs with prescribed curvature.

The paper extends spin geometry to weighted manifolds and defines a new mass for Ricci flow.

The paper defines and analyzes curvature tensors on super twisted product spaces.

Study semilinear equations on weighted manifolds to prove rigidity.

New formulas derived for scalar curvature in generalized Ricci flow.

The paper proves inequalities under Bakry-Émery-Ricci curvature bounds.