A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Study on Kähler manifolds with nonnegative Ricci curvature, focusing on rigidity.
problem Rigidity of Kähler manifolds with nonnegative Ricci curvature.
method Analysis of Kähler manifolds with specific properties.
result Complete noncompact Kähler surface with nonnegative Ricci curvature, Euclidean volume growth, and quadratic curvature decay is biholomorphic to the resolution of an affine algebraic variety.
Study Euler characteristic of manifolds with almost nonnegative curvature operator, showing nonnegativity under certain conditions.
problem Addressing the sign of Euler characteristic for manifolds with almost nonnegative curvature operator.
method Analyzing closed manifolds with uniform upper bounds on curvature operator and applying ANCO-type conditions.
result Nonnegative Euler characteristic for closed 2n-dimensional manifolds with almost nonnegative curvature operator and uniform upper bounds on curvature.
This note is a study of nonnegativity conditions on curvature which are preserved by the Ricci flow. We focus on specific kinds of curvature conditions which we call noncoercive, these are the conditions for which nonnegative curvature and vanishing scalar curvature doesn't imply flatness. We show that, in dimensions g…
We study manifolds with almost nonnegative curvature operator (ANCO) and provide first examples of closed simply connected ANCO mannifolds that do not admit nonnegative curvature operator.
In this paper, we generalize topological results known for noncompact manifolds with nonnegative Ricci curvature to spaces with nonnegative N-Bakry Émery Ricci curvature. We study the Splitting Theorem and a property called the geodesic loops to infinity property in relation to spaces with nonnegative N-Bakry Émery…
We discuss the cobordism type of spin manifolds with nonnegative sectional curvature. We show that in each dimension 4k≥12, there are infinitely many cobordism types of simply connected and nonnegatively curved spin manifolds. Moreover, we raise and analyze a question about possible cobordism obstructions to non…
The paper studies CR Yamabe solutions on Sasakian manifolds with nonnegative curvature.
problem Characterizing CR Yamabe solutions on Sasakian manifolds with nonnegative curvature.
method Analyzes solutions to the CR Yamabe equation in noncompact (2n+1)-dimensional Sasakian manifolds with nonnegative curvature.
result The Heisenberg group H1 is the only (complete) Sasakian space with nonnegative Tanaka-Webster scalar curvature admitting a (nontrivial) positive solution.
The classical Hadamard three circle theorem is generalized to complete Kähler manifolds. More precisely, we show that the nonnegativity of the holomorphic sectional curvature is a necessary and sufficient condition for the three circle theorem. As corollaries, two sharp monotonicity formulae for holomorphic functions a…
In this paper, we prove a general maximum principle for the time dependent Lichnerowicz heat equation on symmetric tensors coupled with the Ricci flow on complete Riemannian manifolds. As an application we construct complete manifolds with bounded nonnegative sectional curvature of dimension greater than or equal to fo…
Given compact Lie groups H\subset G, we study the space of G-invariant metrics on G/H with nonnegative sectional curvature. For an intermediate subgroup K between H and G, we derive conditions under which enlarging the Lie algebra of K maintains nonnegative curvature on G/H. Such an enlarging is possible if (K,H) is a …
The study examines 4D steady gradient Ricci solitons with nonnegative curvature away from a compact set.
problem Analyzing noncompact steady gradient Ricci solitons with nonnegative curvature operator.
method Examining the asymptotic behavior of noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative curvature operator away from a compact set.
result 4D noncompact κ-noncollapsed steady gradient Ricci solitons with nonnegative sectional curvature must be a Bryant Ricci soliton up to scaling.
We construct a compact Kähler manifold of nonnegative quadratic bisectional curvature, which does not admit any Kähler metric of nonnegative orthogonal bisectional curvature. The manifold is a 7-dimensional Kähler C-space with second Betti number equal to 1, and its canonical metric is a Kähler-Einstein metric of posit…
The paper extends a Liouville theorem to biharmonic functions on manifolds with nonnegative Ricci curvature.
problem Proving that biharmonic functions with certain growth conditions are constant or harmonic.
method Using a new local L2 estimate for the Laplacian of biharmonic functions combined with a mean value inequality.
result Any biharmonic function of subquadratic growth on a manifold with nonnegative Ricci curvature must be harmonic, and any of sublinear growth must be constant.
In this paper, we give the sharp upper bound for the number of vertices with positive curvature in a planar graph with nonnegative combinatorial curvature. Based on this, we show that the automorphism group of a planar---possibly infinite---graph with nonnegative combinatorial curvature and positive total curvature is …
We prove a result on equivariant deformations of flat bundles, and as a corollary, we obtain two ``splitting in a finite cover'' theorems for isometric group actions on Riemannian manifolds with infinite fundamental groups, where the manifolds are either compact of nonnegative Ricci curvature, or complete of nonnegativ…
We find new obstructions to the existence of complete Riemannian metric of nonnegative sectional curvature on manifolds with infinite fundamental groups. In particular, we construct many examples of vector bundles whose total spaces admit no nonnegatively curved metric.
We show that a certain family of cohomogeneity one manifolds does not admit an invariant metric of nonnegative sectional curvature, unless it admits one with positive curvature. As a consequence, the classification of nonnegatively curved cohomogeneity one manifolds in dimension 7 is reduced to only one further family …
In this note, we consider the isoperimetric inequality on an asymptotically flat manifold with nonnegative scalar curvature, and improve it by using Hawking mass. We also obtain a rigidity result when equality holds for the classical isoperimetric inequality on an asymptotically flat manifold with nonnegative scalar cu…
We describe a construction of Riemannian metrics of nonnegative sectional curvature on a closed smooth nonorientable 4-manifold with fundamental group of order two that realizes a homotopy class that was not previously known to contain nonnegatively curved manifolds. The procedure yields new metrics of nonnegative sect…
The study examines mean curvature flow and Heegaard surfaces in lens spaces.
problem Analyzing mean convex two-spheres and Heegaard tori in lens spaces.
method Proves path-connectedness of moduli spaces of mean convex two-spheres and Heegaard tori in manifolds with nonnegative Ricci curvature.
result There are always either one or two path components of mean convex Heegaard tori in lens spaces, depending on the ambient manifold's homotopy type.
In a previous paper, we constructed complete manifolds of positive Ricci curvature with quadratically asymptotically nonnegative curvature and infinite topological type but dimension ≥6. The purpose of the present paper is to use a different way to exhibit a family of complete I-dimensinal (I≥5) Riemannian m…