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.
Derives generalizations of the long neck principle and spectral width inequality.
Proves existence of special metrics on curved spaces.
We discuss two generalizations of the collar lemma. The first is the stable neighborhood theorem which says that a (not necessarily simple) closed geodesic in a hyperbolic surface has a \lq\lq stable neighborhood\rq\rq whose width only depends on the length of the geodesic. As an application, we show that there is a lo…
The paper extends the collar theorem to non-compact surfaces using new comparison theorems.
Proves principles and estimates for initial data sets in Einstein equations.
New examples show manifolds with noncompact boundaries that can't be pseudo-collarable.
Positive representations on surfaces have positive cross-ratios and satisfy a collar lemma.
The notion of an open collar is generalized to that of a pseudo-collar. Important properties and examples are discussed. The main result gives conditions which guarantee the existence of a pseudo-collar structure on the end of an open n-manifold (n > 6). This paper may be viewed as a generalization of Siebenmann's famo…
In this article, we prove an analog of the classical collar lemma in the setting of Hitchin representations.
Develops a broader approach to pseudo-collar constructions.
Collar lemma proven for certain surface group representations.
In this note we define the notion of collarable slices of Lagrangian submanifolds. Those are slices of Lagrangian submanifolds which can be isotoped through Lagrangian submanifolds to a cylinder over a Legendrian embedding near a contact hypersurface. Such a notion arises naturally when studying intersections of Lagran…
Characterizes pseudo-collarable manifolds with noncompact boundaries.
In this paper, we develop a geometric procedure for producing a reverse to Quillen's plus construction, a construction called a 1-sided h-cobordism or semi-h-cobordism. We then use this reverse to the plus construction to produce uncountably many distinct ends of manifolds called pseudo-collars, which are stackings of …
Study of harmonic maps from degenerating surfaces with free boundary.
The paper solves conditions for extending circle-valued Morse functions.
We consider an arbitrary linear elliptic first--order differential operator A with smooth coefficients acting between sections of complex vector bundles E,F over a compact smooth manifold M with smooth boundary N. We describe the analytic and topological properties of A in a collar neighborhood U of N and analyze vario…
The paper connects curvature data to polynomial coefficients in gluing formulas.
Study parabolicity of Riemann surfaces via Fenchel-Nielsen parameters.
This paper concerns a formula which relates the Lefschetz number L(f) for a map f:M --> M' to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of M. Here M is a compact manifold and M' is M with a collar attached.
In this paper, we recall Quillen's plus construction for high-dimensional smooth manifolds and the solution to the group extension problem. We then develop a geometric procedure due for producing a "reverse" to the plus construction, a one-sided s-cobordism called a semi-s-cobordism, when the total group of the group e…
In this paper, we obtain analogues of Jorgensen's inequality for non-elementary groups of isometries of quaternionic hyperbolic -space generated by two elements, one of which is loxodromic. Our result gives some improvement over earlier results of Kim [10] and Markham [15]}. These results also apply to complex hyper…
We continue our study of ends non-compact manifolds. The over-arching aim is to provide an appropriate generalization of Siebenmann's famous collaring theorem that applies to manifolds having non-stable fundamental group systems at infinity. In this paper a primary goal is finally achieved; namely, a complete character…
For compact Riemann surfaces, the collar theorem and Bers' partition theorem are major tools for working with simple closed geodesics. The main goal of this paper is to prove similar theorems for hyperbolic cone-surfaces. Hyperbolic two-dimensional orbifolds are a particular case of such surfaces. We consider all cone …
The paper establishes distance estimates for manifolds with lower scalar curvature bounds.
Dehn's Lemma for loops in 3-manifolds.
In this paper we prove a new version of the Schoenflies extension theorem for collared domains in Euclidean n-space: for 1 < p < n, locally bi-Lipschitz homeomorphisms between collared domains with locally p-integrable, second-order weak derivatives admit homeomorphic extensions of the same regularity. Moreover, the th…
Paper simplifies a theorem without curvature, generalizing previous work.
Research extends a function to a non-orientable 3-manifold without critical points.
Stability of Morse index for harmonic maps on degenerating surfaces analyzed.
We use Furuta's result, usually referred to as ``10/8-conjecture'', to show that for any compact 3-manifold the open manifold $M\times\r$ has infinitely many different smooth structures. Another consequence of Furuta's result is existence of infinitely many smooth structures on open topological 4-manifolds with a t…
We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundl…
New examples of non-smoothable homeomorphisms of 4-manifolds with boundary found.
Positive representations of surface groups in PO(p,q) form connected components of character varieties.
The paper sets geometric lower bounds for low Steklov eigenvalues on manifolds.
Sharp eigenvalue estimates on degenerating hyperbolic surfaces.
Arithmetic spaces simplified to simplicial complexes.
Proves a theorem for normal distributions on manifolds with boundary.
Deep learning classifies animal behavior from wearable accelerometers.
Study shows caste's reduced importance in predicting women's work status and type.
Study applies Penrose and mass theorems to -manifolds with nonnegative scalar curvature and CMC boundary.
Let be a real closed field. We define the notion of a maximal framing for a representation of the fundamental group of a surface with values in . We show that ultralimits of maximal representations in admit such a framing, and that all maximal framed represen…
In this paper we continue an earlier study of ends non-compact manifolds. The over-arching goal is to investigate and obtain generalizations of Siebenmann's famous collaring theorem that may be applied to manifolds having non-stable fundamental group systems at infinity. In this paper we show that, for manifolds with c…
New coordinates for Teichmüller space compactification.
The study explores deep and shallow slice knots in 4-manifolds, linking them to conjectures and proving existence and nonexistence results.
Researchers approximate spectral targets on manifolds with constant negative curvature.
We show that if the totally geodesic boundary of a compact hyperbolic 3-manifold M has a large collar of depth d, then the diameter of the skinning map of M is no more than A exp(-d) for some A depending only on the genus and injectivity radius of the boundary of M.
We establish an energy quantization result for sequences of Willmore surfaces when the underlying sequence of Riemann surfaces is degenerating in the moduli space. we notably exhibit a new residue which quantifies the potential loss of energy in collar regions. Thanks to these residues, we also prove compactness of Wil…