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 high-codimensional minimal surfaces in hyperbolic space.
Proves existence of curved surfaces in hyperbolic space.
New formulas for hyperbolic mass using horospheres.
Abstract reviews hyperbolic positive energy theorems.
Solves the asymptotic Plateau problem in hyperbolic space for specific curvature.
Study on eigenvalue rate of geodesic balls in asymptotically hyperbolic Einstein manifolds.
Defines renormalized volume for bounded regions in asymptotically hyperbolic Einstein spaces.
Compactifies CR structures for complex hyperbolic manifolds.
Proves positive mass theorems for specific types of curved spaces.
We give estimates on asymptotic dimensions of products of general hyperbolic spaces with following applications to the hyperbolic groups. We give examples of strict inequality in the product theorem for the asymptotic dimension in the class of the hyperbolic groups; and examples of strict inequality in the product theo…
Smooth solutions found for a curvature problem in hyperbolic space.
We show that the constant mean curvature hypersurfaces in the hyperbolic n-space spanning the boundary of a star shaped C^{1,1} domain in the asymptotic sphere give a foliation of the hyperbolic n-space. We also show that if C is a closed codimension-1 C^{2,a} submanifold in the asymptotic sphere bounding a unique cons…
Study of constant curvature hypersurfaces in hyperbolic space.
Harmonic maps from hyperbolic planes to hyperbolic space exist with given boundary data.
Study on hyperbolic manifolds with special boundaries.
Study minimal surfaces in complex hyperbolic space, linking entropy and volume.
Asymptotic subcone of an unbounded metric space is another metric space, capturing the structure of the original space at infinity. In this paper we define a functional metric space S which is an asymptotic subcone of the hyperbolic plane. This space is a real tree branching at every its point. Moreover, it is a homoge…
Study calculates spectra of minimal hypersurfaces in hyperbolic space.
Stability of positive mass theorem for hyperbolic manifolds studied.
We introduce a new quasi-isometry invariant of metric spaces called the hyperbolic dimension, hypdim, which is a version of the Gromov's asymptotic dimension, asdim. The hyperbolic dimension is at most the asymptotic dimension, however, unlike the asymptotic dimension, the hyperbolic dimension of any Euclidean space R^…
Proves Laplacian and Lichnerowicz Laplacian are sectorial in weighted Hölder spaces.
Sharp eigenvalue estimates for submanifolds of asymptotically hyperbolic spaces.
Constructs an asymptotic metric for moduli space of centred hyperbolic monopoles.
Paper estimates curvature of semi-convex hypersurfaces in hyperbolic space.
Local X-ray transform works well near boundaries in hyperbolic spaces.
Defines mass for non-smooth hyperbolic spaces using a modified flow.
We prove a positive mass theorem for complete Kähler manifolds that are asymptotic to the complex hyperbolic space.
Generalizing the result of Li and Tam for the hyperbolic spaces, we prove an existence theorem on the Dirichlet problem for harmonic maps with boundary conditions at infinity between asymptotically hyperbolic manifolds.
We prove that all hierarchically hyperbolic spaces have finite asymptotic dimension and obtain strong bounds on these dimensions. One application of this result is to obtain the sharpest known bound on the asymptotic dimension of the mapping class group of a finite type surface: improving the bound from exponential to …
It is extended a result due to B. Guan and J. Spruck on the asymptotic Plateau's problem for CMC radial graphs in hyperbolic space to horizontal CMC graphs.
Any Kaehler metric on the ball which is strongly asymptotic to complex hyperbolic space and whose scalar curvature is no less than the one of the complex hyperbolic space must be isometrically biholomorphic to it. This result has been known for some time in odd complex dimension and we provide here a proof in even dime…
We prove the rigidity of positive mass theorem for asymptotically hyperbolic manifolds. Namely, if the mass equality holds, then the manifold is isometric to hyperbolic space. The result was previously proven for spin manifolds or under special asymptotics.
Asymptotic property C was introduced by Dranishnikov to study spaces with infinite asymptotic dimension. We show that asymptotic property C is preserved by infinite products. We also show that countable restricted direct products of countable groups with finite asymptotic dimension have asymptotic property C. Then we i…
Solves Yamabe problem for Sobolev-class asymptotically hyperbolic manifolds.
Study submanifolds in hyperbolic space, focusing on their boundary and Laplace operator.
We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyper…
In this article, we classify the set of asymptotic mass-like invariants for asymptotically hyperbolic metrics. It turns out that the standard mass is just one example (but probably the most important one) among the two families of invariants we find. These invariants are attached to finite-dimensional representations o…
Two curves in hyperbolic space share a bounded distance, leading to a minimizing surface.
New theorem finds new minimal hypersurfaces in hyperbolic space.
We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recentl…
In this paper we study asymptotically hyperbolic manifolds given as graphs of asymptotically constant functions over hyperbolic space $\bH^n$. The graphs are considered as subsets of $\bH^{n+1}$ and carry the induced metric. For such manifolds the scalar curvature appears in the divergence of a 1-form involving the int…
For asymptotically hyperbolic manifolds of dimension with scalar curvature at least equal to the conjectured positive mass theorem states that the mass is non-negative, and vanishes only if the manifold is isometric to hyperbolic space. In this paper we study asymptotically hyperbolic manifolds which are …
Generalising a proof by Bartnik in the asymptotically Euclidean case, we give an elementary proof of positivity of the hyperbolic mass near the hyperbolic space. It is a pleasure to dedicate this work to Robert Bartnik on the occasion of his 60th birthday.
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
Extends flat submanifold properties from hyperbolic plane to symmetric spaces.
We introduce a quasi-symmetry invariant of a metric space Z called the capacity dimension. Our main result says that for a visual Gromov hyperbolic space X the asymptotic dimension of X is at most the capacity dimension of its boundary at infinity plus 1.
Paper finds invariant solutions for Plateau problem in hyperbolic space.
Study calculates mass of special polyhedra in hyperbolic space.