New formulas for hyperbolic mass using horospheres.
problem Mass calculation of asymptotically hyperbolic manifolds.
method Geometric formulas derived using coordinate horospheres.
result Improved rigidity results of hyperbolic space.
On-device research index
arXiv research
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.
168,695 papers · 148 categories
Trend · papers per month
48 results for “hyperbolic mass”
Proves positive mass theorems for specific types of curved spaces.
problem Analyzing mass in curved spaces with boundaries.
method Proves positive mass theorems for specific types of curved spaces with boundaries.
result Establishes conditions under which mass is positive in these spaces.
Study calculates mass of special polyhedra in hyperbolic space.
problem Evaluating mass in hyperbolic geometry.
method Used upper half space model and special polyhedra.
result Evaluated mass functional on polyhedra.
A definition of the mass aspect function for weakly regular asymptotically hyperbolic manifoldsmath.DG
Unified definition of mass aspect function for weakly regular hyperbolic manifolds.
problem Ambiguity in mass definition for asymptotically hyperbolic manifolds.
method Introduced an ADM-style mass aspect function for broad asymptotics and low regularity.
result Unified mass aspect function exhibits favorable covariance properties.
Surveying mass in 2D hyperbolic geometry, overcoming challenges via minimisation.
problem Defining mass in 2D hyperbolic geometry.
method Minimisation using positive energy theorem and gluing theorems.
result Construction of novel initial data sets with controlled mass.
Defines mass for non-smooth hyperbolic spaces using a modified flow.
problem Defining mass for non-smooth, asymptotically hyperbolic spaces.
method Normalized Ricci-DeTurck flow with scalar curvature lower bound.
result Mass function well-defined for continuous metrics.
Paper defines Bartnik mass for hyperbolic extensions and proves staticity.
problem Defining and proving staticity of asymptotically hyperbolic minimal mass extensions.
method Definition of Bartnik mass, construction of metrics, one-parameter family analysis.
result Static potential for asymptotically hyperbolic admissible extensions achieving Bartnik mass.
Stability of positive mass theorem for hyperbolic manifolds studied.
problem Stability of the positive mass theorem for asymptotically hyperbolic manifolds.
method Adapted intrinsic flat distance approach to show stability for a class of manifolds.
result Stability of the positive mass theorem for a class of asymptotically hyperbolic graphical manifolds.
We consider the evolution of the asymptotically hyperbolic mass under the curvature-normalized Ricci flow of asymptotically hyperbolic, conformally compactifiable manifolds. In contrast to asymptotically flat manifolds, for which ADM mass is constant during Ricci flow, we show that the mass of an asymptotically hyperbo…
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 …
New solutions found with negative mass in general relativity.
problem Finding metrics with negative mass in general relativity.
method Constructing families of metrics with specific properties.
result Obtained new classes of solutions with negative mass.
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.
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…
Spectral Positive Mass Theorem for Asymptotically Hyperbolic 3-manifolds with Toroidal Infinitymath.DG
Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
problem Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
method Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
result Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.
Solves Jang equation for hyperboloidal data, proving positive mass theorem.
problem Proving the positive mass theorem in asymptotically hyperbolic 3D spacetimes.
method Solves Jang equation with hyperboloidal initial data, applies to positive mass theorem.
result Non-spinor proof of positive mass theorem in 3D asymptotically hyperbolic spacetimes.
Defines a new geometric quantity for hyperbolic manifolds, showing it's well-defined and invariant.
problem Defining a mass for asymptotically hyperbolic manifolds under weaker conditions.
method Volume-renormalized mass defined as a linear combination of ADM mass and renormalized volume.
result Volume-renormalized mass is well-defined and diffeomorphism invariant under weaker conditions.
Study glues 2D hyperbolic manifolds, deriving mass formulas.
problem Mass invariance and positivity for 2D hyperbolic manifolds.
method Maskit gluing construction, minimization, monodromy construction.
result Derive mass/entropy formulae for glued manifolds.
The paper consists of two parts. In the first part, by using the Gauss-Bonnet curvature, which is a natural generalization of the scalar curvature, we introduce a higher order mass, the Gauss-Bonnet-Chern mass $m^{\H}_k$, for asymptotically hyperbolic manifolds and show that it is a geometric invariant. Moreover, we pr…
The mass of asymptotically hyperbolic ends and manifolds is analyzed.
problem Analyzing the mass of asymptotically hyperbolic ends and manifolds.
method Using Riemannian spin manifolds, scalar curvature, and mean curvature.
result The mass of an asymptotically hyperbolic end is timelike future-directed or zero.
Simplified proof of mass center system's uniqueness and generalized Pappus' theorem across Euclidean, spherical, and hyperbolic geometries.
problem Proving the uniqueness of the mass center system in non-Euclidean geometries and deriving a generalized Pappus' theorem.
method Revisiting and simplifying G.A. Galperin's proof, extending the mass center system to manifolds, and deriving a generalized Pappus' theorem.
result Unified and simpler proofs for Pappus' theorem in Euclidean, spherical, and hyperbolic geometries.
In this paper, we will show that the limit of some quasilocal mass integrals of the coordinate spheres in an asymptotically hyperbolic (AH) manifold is the mass integral of the AH manifold. This is the analogue of the well known result that the limit of the Brown-York mass of coordinate spheres is the ADM mass in an as…
The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy condition without a cosmological constant. There is a natural analogue of the Bartnik…
Solves Jang's equation for hyperboloidal data in 4-7 dimensions, proving positive mass theorem.
problem Proving the positive mass theorem for asymptotically hyperbolic initial data sets in specific dimensions.
method Solves Jang's equation with hyperboloidal initial data in dimensions 4-7.
result Non-spinor proof of the positive mass theorem in 4-7 dimensions.
We prove a positive mass theorem for complete Kähler manifolds that are asymptotic to the complex hyperbolic space.
In 1996, Huisen-Yau proved that every three-dimensional, asymptotically Schwarzschilden manifold with positive mass is uniquely foliated by stable spheres of constant mean curvature and they defined the center of mass using this CMC-foliation. Rigger and Neves-Tian showed in 2004 and 2009/10 analogous existence and uni…
New positive mass theorem for hyperbolic 3-manifolds using Green functions.
problem Proving a positive mass theorem for asymptotically hyperbolic 3-manifolds.
method Using a monotonicity formula for the Green function of the Laplace operator.
result Established a new positive mass theorem for three-dimensional manifolds.
Paper proves stability of positive mass theorem for specific types of manifolds.
problem Stability of positive mass theorem for compact graphical manifolds.
method Used Federer--Fleming flat distance and static quasi-local Brown-York energy.
result Proved stability of positive mass theorem for compact (locally) hyperbolic graphical manifolds.
We define a mass-type invariant for asymptotically hyperbolic manifolds with a noncompact boundary which are modelled at infinity on the hyperbolic half-space and prove a sharp positive mass inequality in the spin case under suitable dominant energy conditions. As an application we show that any such manifold which is …
Proves positive mass theorem for hyperbolic manifolds with ends.
problem Establishing positive mass theorem for complex initial data sets.
method Used spectral PSC, Jang equation, and quantitative shielding theorem.
result Proved positive mass theorem for asymptotically hyperbolic manifolds.
The Witten spinorial argument has been adapted in several works over the years to prove positivity of mass in the asymptotically AdS and asymptotically hyperbolic settings in arbitrary dimensions. In this paper we prove a scalar curvature rigidity result and a positive mass theorem for asymptotically hyperbolic manifol…
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.
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…
On asymptotically flat and asymptotically hyperbolic manifolds, by evaluating the total mass via the Ricci tensor, we show that the limits of certain Brown-York type and Hawking type quasi-local mass integrals equal the total mass of the manifold in all dimensions.
We present a set of global invariants, called "mass integrals", which can be defined for a large class of asymptotically hyperbolic Riemannian manifolds. When the "boundary at infinity" has spherical topology one single invariant is obtained, called the mass; we show positivity thereof. We apply the definition to confo…
In the asymptotically locally hyperbolic setting it is possible to have metrics with scalar curvature at least -6 and negative mass when the genus of the conformal boundary at infinity is positive. Using inverse mean curvature flow, we prove a Penrose inequality for these negative mass metrics. The motivation comes fro…
New metrics found in hyperbolic manifolds as volume-minimizers.
problem Finding critical points of volume-renormalized mass.
method Critical points of the volume-renormalized mass over asymptotically hyperbolic manifolds.
result V-static metrics are critical points of volume-renormalized mass.
Researchers compute quasi-local mass of Kerr black hole horizon.
problem Computing the quasi-local mass of Kerr black hole horizons.
method Isometric embedding of Kerr black hole horizon in hyperbolic space.
result Quasi-local mass varies with Kerr black hole spin parameter.
We establish versions of the Positive Mass and Penrose inequalities for a class of asymptotically hyperbolic hypersurfaces. In particular, under the usual dominant energy condition, we prove in all dimensions an optimal Penrose inequality for certain graphs in hyperbolic space whose boundary…
Mass in relativity linked to polyhedra geometry.
problem Mass in general relativity.
method Riemannian polyhedra geometry.
result Mass connected to polyhedra geometry.
We show that the mass of an asymptotically hyperbolic manifold with a noncompact boundary can be evaluated via the Ricci tensor and the second fundamental form by using purely coordinates. The method is analog to Miao-Tam's approach to the asymptotically flat manifold.
We prove a positive mass theorem for some noncompact spin manifolds that are asymptotic to products of hyperbolic space with a compact manifold. As conclusion we show the Yamabe inequality for some noncompact manifolds which are important to understand the behaviour of Yamabe invariants under surgeries.
Regularity of inverse mean curvature flow in asymptotically hyperbolic manifolds with dimension math.DG
By making use of the nice behavior of Hawking masses of slices of a weak solution of inverse mean curvature flow in three dimensional asymptotically hyperbolic manifolds, we are able to show that each slice of the flow is star-shaped after a long time, and then we get the regularity of the weak solution of inverse mean…
Study shows rigidity of polyhedrons in hyperbolic spaces.
problem Rigidity of polyhedrons in hyperbolic spaces.
method Extending Gromov's comparison theory to metrics with negative scalar curvature lower bounds.
result Localization of the positive mass theorem for asymptotically hyperbolic manifolds.
W. Simon proved a conformal positive mass theorem, which was used to prove uniqueness of black holes later. In this note, we will generalize Simon's conformal positive mass theorem in two directions. First we will consider spacetime version of conformal positive mass theorems on asymptotically flat initial data set. Ne…
The paper proves a positive mass theorem for non-compact static domains in hyperbolic space.
problem Proving a positive mass theorem for non-compact static domains in hyperbolic space.
method Formulating and proving a positive mass theorem under natural dominant energy conditions, using elliptic boundary conditions on spinors.
result Retrieve a sharper version of a recent result by Souam about the rigidity of non-compact static domains.
New positive mass theorems for ALH manifolds with toroidal ends.
problem Proving positive mass theorems for asymptotically locally hyperbolic manifolds.
method Utilizes properties of marginally outer trapped surfaces and a new technique involving μ-bubbles.
result Obtained new positive mass theorems for asymptotically locally hyperbolic manifolds without boundary.
Paper bounds total geodesic curvature using boundary data in hyperbolic gravity.
problem Bounding total geodesic curvature in a hyperbolic setting.
method Derives an upper bound for total geodesic curvature in terms of boundary data.
result Upper bound for total geodesic curvature expressed solely in terms of boundary data.
New method calculates volume-renormalized mass from Hamiltonian perspective.
problem Calculating volume-renormalized mass for asymptotically hyperbolic manifolds.
method Using Michel's mass invariants and a reduced Hamiltonian perspective, the volume-renormalized mass is deduced.
result The reduced Hamiltonian recovers the volume-renormalized mass and its variations.