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.
We study a properly convex real projective manifold with (possibly empty) compact, strictly convex boundary, and which consists of a compact part plus finitely many convex ends. We extend a theorem of Koszul which asserts that for a compact manifold without boundary the holonomies of properly convex structures form an …
Let K be a connected Lie group and M a Hamiltonian K-manifold. In this paper, we introduce the notion of convexity of M. It implies that the momentum image is convex, the moment map has connected fibers, and the total moment map is open onto its image. Conversely, the three properties above imply convexity. We show tha…
3-manifold groups can only have convex co-compact representations if they are geometric or hyperbolic.
problem Understanding which 3-manifold groups can have convex co-compact representations.
method Analyzing representations of 3-manifold groups into projective general linear group, focusing on convex co-compactness.
result Fundamental groups of closed irreducible orientable 3-manifolds can only admit convex co-compact representations if they are geometric or hyperbolic.
This study of properly or strictly convex real projective manifolds introduces notions of parabolic, horosphere and cusp. Results include a Margulis lemma and in the strictly convex case a thick-thin decomposition. Finite volume cusps are shown to be projectively equivalent to cusps of hyperbolic manifolds. This is pro…
In order to obtain a closed orientable convex projective four-manifold with small positive Euler characteristic, we build an explicit example of convex projective Dehn filling of a cusped hyperbolic four-manifold through a continuous path of projective cone-manifolds.
A characterization of the proximal normal cone is obtained and a separation theorem for convex subsets of Riemannian manifolds is established. Moreover, the convexity of the distance function dS for a convex subset S in the cases where the boundary of S contains a geodesic segment, the boundary of S is C2 o…
This paper extends a 3D result to higher dimensions for manifolds with positive curvature.
problem Proving higher-dimensional manifolds with positive curvature operator and strictly convex boundary are diffeomorphic to the Euclidean disk.
method Using the positive curvature operator and strictly convex boundary conditions to deduce the manifold's diffeomorphism to the Euclidean disk.
result Compact n-manifolds with positive curvature operator and strictly convex boundary are diffeomorphic to the standard n-dimensional Euclidean disk.
3-manifolds with convex boundary are rigid in certain curvature conditions.
problem Characterizing the rigidity of nonpositively curved manifolds with convex boundaries.
method Using a comparison formula for total curvature of Riemannian hypersurfaces, the authors prove the rigidity of the manifolds.
result Compact Riemannian 3-manifolds with strictly convex simply connected boundary and sectional curvature K≤a≤0 are isometric to a convex domain in a complete simply connected space of constant curvature a.
We show that a non-compact (forward) complete Finsler manifold whose Holmes- Thompson volume is infinite admits no non-trivial convex functions. We apply this result to some Finsler manifolds whose Busemann function is convex.
In this paper we show that bending a finite volume hyperbolic d-manifold M along a totally geodesic hypersurface Σ results in a properly convex projective structure on M with finite volume. We also discuss various geometric properties of bent manifolds and algebraic properties of their fundamental groups. We th…
The study proves conditions for convex hypersurfaces in Riemannian manifolds to be rational homology spheres.
problem Conditions for convex hypersurfaces to be rational homology spheres in Riemannian manifolds.
method The study proves conditions for convex hypersurfaces in Riemannian manifolds to be rational homology spheres using vanishing and estimation theorems for Betti numbers.
result Conditions for convex hypersurfaces to be rational homology spheres in Riemannian manifolds.
The main goal of this paper is to present results of existence and non-existence of convex functions on Riemannian manifolds and, in the case of the existence, we associate such functions to the geometry of the manifold. Precisely, we prove that the conservativity of the geodesic flow on a Rieman- nain manifold with in…
The usual notion of set-convexity, valid in the classical Euclidean context, metamorphoses into several distinct convexity types in the more general Riemannian setting. By studying this phenomenon in reverse, we characterize complete manifolds for which certain convexity types are assumed a priori to coincide.
We prove the existence of free boundary minimal annuli inside suitably convex subsets of three-dimensional Riemannian manifolds with nonnegative Ricci curvature − including strictly convex domains of the Euclidean space R3.
Given a Riemannian manifold M and a hypersurface H in M, it is well known that infinitesimal convexity on a neighborhood of a point in H implies local convexity. We show in this note that the same result holds in a semi-Riemannian manifold. We make some remarks for the case when only timelike, null or spacelike geodesi…
Locally convex compact immersed hypersurfaces in Finsler-Hadamard manifolds with bounded T-curvature are considered. We prove that such hypersurfaces are embedded as the boundary of convex body under certain conditions on the normal curvatures