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.
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48 results for “upper half-space model”
Inverse metric matrices on Siegel-Jacobi spaces are calculated for Berezin quantization.
problem Calculating inverse metric matrices on Siegel-Jacobi spaces.
method Inversion of metric matrices on and .
result Explicit calculations of inverse metric matrices for .
New geometry based on Siegel upper half-space with volume formula.
problem Developing a new 3D geometry based on Siegel upper half-space.
method Constructing a geometry fibered over Siegel upper half-space and providing a volume formula.
result Volume of Siegel-Seifert closed manifolds is the fiber circle length times base manifold's Euler characteristic.
The paper classifies and describes five-sided hyperbolic polyhedra with one ideal vertex.
problem Classifying five-sided hyperbolic polyhedra with one ideal vertex.
method Using lines and circles in the plane to find each polyhedron in the upper half-space model, and generating matrix generators for the reflection groups.
result Matrix generators for the orientation-preserving subgroup of each corresponding reflection group.
Extended metric defined on Siegel-Jacobi space using invariant forms.
problem Defining a metric on the extended Siegel-Jacobi upper half space.
method Matrix embedding, pre-Iwasawa decomposition, invariant forms, sum of squares of forms.
result Invariant metric on the extended Siegel-Jacobi upper half space is derived.
Developed a half-space model for pseudo-hyperbolic space.
problem Modeling pseudo-hyperbolic space for any dimensions.
method Created an isometric embedding of pseudo-hyperbolic space into a half-space.
result Geodesics, totally geodesic submanifolds, horospheres, and isometry group are described in the half-space model.
Fundamental solutions of Dirac type operators are introduced for a class of conformally flat manifolds. This class consists of manifolds obtained by factoring out the upper half-space of by arithmetic subgroups of generalized modular groups. Basic properties of these fundamental solutions are presented t…
The paper confirms a conjecture about Hardy-Sobolev-Maz'ya inequalities and Green's functions on hyperbolic spaces.
problem Sharp constant in Hardy-Sobolev-Maz'ya inequalities and Green's functions on hyperbolic spaces.
method Fourier analysis techniques on hyperbolic spaces and Green's function estimates.
result The sharp constant in the -th order Hardy-Sobolev-Maz'ya inequality in the upper half space of dimension coincides with the best -th order Sobolev constant when is odd and .
Proposes NUV priors for half-space and box constraints.
problem Adding constraints to linear Gaussian models without computational cost.
method Introduces NUV representations for half-space and box constraints.
result Adds constraints to linear Gaussian models without affecting computational tractability.
Paper classifies critical points in half-space with new distance function.
problem Classifying critical points in half-space with capillary CMC hypersurfaces.
method New shifted distance function for capillary problem in half-space.
result Proves Alexandrov-type theorem for singular capillary CMC hypersurfaces.
Paper studies stability of curved surfaces in a half-space.
problem Stability of anisotropic capillary hypersurfaces in a half-space.
method Analyzes weak stability and proves Bernstein-type theorems.
result Compact hypersurfaces are stable if and only if they are a truncated Wulff shape.
Paper introduces capillary Schwarz symmetrization in half-space.
problem Capillary problems in half-space.
method Introduces a special anisotropic gauge to transform capillary symmetrization to convex symmetrization.
result Capillary Schwarz symmetrization in half-space established.
The paper establishes inequalities for -capacitary functions in flat half-spaces.
problem Understanding -capacitary functions in asymptotically flat half-spaces.
method Establishes monotone quantities and mass-capacity inequalities.
result Sharp inequalities attain equality on a Schwarzschild half-space.
Study proves no nontrivial minimal surfaces in half-space with specific boundary conditions.
problem Proving the nonexistence of minimal surfaces in half-space with certain boundary conditions.
method Analyzes minimal surface equations in half-space with specific boundary conditions.
result Establishes Liouville type theorems for minimal surfaces in half-space.
Paper analyzes iterative learning for concept classes and learns half-spaces.
problem Learning concept classes efficiently with iterative learners.
method Analyzes various settings of iterative learning and provides a constructive algorithm for half-spaces.
result Constructive iterative algorithm for learning half-spaces from informant.
Anisotropic minimal graphs over half-spaces are flat.
problem Characterizing minimal graphs over half-spaces.
method Maximum principle and fully nonlinear PDE theory.
result Anisotropic minimal graphs over half-spaces are flat.
Study an anisotropic capillary flow to solve capillary Orlicz-Minkowski problem.
problem Solve capillary Orlicz-Minkowski problem without evenness assumption.
method Analyze an anisotropic capillary Gauss curvature flow to prove convergence and establish existence.
result Establish existence result for capillary Orlicz-Minkowski problem without evenness assumption.
Study proves no minimal surfaces can be contained in certain half-spaces or cones.
problem Prohibiting minimal surfaces from certain geometric configurations.
method Analyzes weighted minimal surfaces in with height-dependent weights.
result No proper surfaces can be contained in specific half-spaces or cones.
Study on minimal surfaces with free boundary in a half-space, improving index estimates.
problem Non-existence of index two embedded minimal surfaces with free boundary in a half-space.
method Improved estimates of Neumann and Dirichlet indices, simplified proof of lower bounds.
result Answered Ambrozio et al.'s question and provided new lower bounds.
Paper proves flatness of anisotropic minimal graphs in half-spaces.
problem Anisotropic minimal graphs with free boundaries in half-spaces.
method Proves flatness using linear growth conditions.
result Anisotropic minimal graphs in half-spaces are flat if they have at most one-sided linear growth.
We investigate a potential obtained as the convolution of a radially symmetric function and the characteristic function of a body (the closure of a bonded open set) with exterior cones. In order to restrict the location of a maximizer of the potential into a smaller closed region contained in the interior of the body, …
The study proves properties of capillary graphs in half-spaces.
problem Characterizing capillary minimal graphs in half-spaces.
method Analyzing tangent cones and regular set properties.
result Capillary minimal graphs in low dimensions or specific cone conditions are linear.
Alexandrov-Fenchel inequalities for convex hypersurfaces in the half-space with capillary boundarymath.DG
Paper solves inequalities for capillary hypersurfaces in half-spaces.
problem Finding inequalities for convex capillary hypersurfaces in half-spaces.
method Introduced quermassintegrals and constructed a new locally constrained curvature flow to prove convergence to spherical caps.
result Obtained Alexandrov-Fenchel inequalities for convex capillary hypersurfaces.
New theorem for nonlocal minimal surfaces in any dimension.
problem Classical half-space theorems for minimal surfaces.
method Established a new half-space theorem.
result Result holds in any dimension.
This study proves the Half Space Property for RCD(0,N) and RCD(K,N) spaces.
problem Proving the Half Space Property for RCD(K,N) spaces.
method Analyzing locally perimeter minimizing sets and extending Green's functions results.
result The Half Space Property holds for RCD(K,N) spaces under specific conditions.
Researchers prove rigidity of convex polytopes in hyperbolic space using spinor techniques.
problem Proving rigidity of convex polytopes in hyperbolic space.
method Spinor techniques and recent smoothing constructions of Brendle-Wang.
result Scalar curvature rigidity for parabolic convex polytopes in hyperbolic space.
New Minkowski inequality for capillary surfaces in half-space.
problem Establishing a new Minkowski inequality for capillary surfaces.
method Flow of inverse mean curvature type for capillary hypersurfaces in a half-space.
result Derive a new Minkowski-type inequality for star-shaped and mean convex capillary hypersurfaces.
We propose a simple proof of the vertical half-space theorem for Heisenberg space.
Paper extends Wente's result to anisotropic capillary surfaces in half-spaces.
problem Extending Wente's result to anisotropic capillary surfaces.
method New Heintze-Karcher inequality and Minkowski formula.
result Anisotropic capillary hypersurfaces in half-spaces are Wulff shapes.
The paper classifies solutions to a Liouville equation on a half-space with a specific boundary condition.
problem Classifying solutions to a Liouville equation with a nonlinear Neumann boundary condition.
method Analyzing the -Laplacian Liouville equation on the half-space with positive nonlinear Neumann boundary condition.
result The classification of solutions extends previous results for and .
On the topology of H(2)math.GT
In this paper, we first single out a proper subgroup Γof Sp(4,Z) generated by three elements, which arises from the parallelogram decompositions of translation surfaces in H(2). We then prove that the space H(2)/C* can be identified to the quotient J_2/Γ, where J_2 is the Jacobian locus in the Siegel upper half space H…
The paper proves inequalities for convex capillary hypersurfaces in a half-space.
problem Proving inequalities for convex capillary hypersurfaces in a half-space.
method Locally constrained inverse curvature flow with spherical cap convergence.
result Proves a complete family of Alexandrov-Fenchel inequalities for convex capillary hypersurfaces.
Study on convex capillary hypersurfaces with Lp curvature in half-space.
problem Prescribed Lp curvature for convex capillary hypersurfaces.
method Reduction to Hessian quotient equation with Robin boundary condition.
result Existence and uniqueness of smooth admissible solutions.
Solves capillary -Christoffel-Minkowski problem in half-space.
problem Capillary surfaces in half-space geometry.
method Non-collapsing estimate for height and capillary support function.
result Extends Christoffel-Minkowski existence result.
Capillary Minkowski Flowsmath.AP
Study flows for capillary Minkowski problems in half-spaces.
problem Existence and behavior of capillary Minkowski problems.
method Anisotropic capillary Gauss curvature flows.
result Long-time existence and asymptotic behavior of flows.
Solves Christoffel-Minkowski problem for capillary convex bodies in Euclidean half-space.
problem Finding capillary convex bodies with prescribed -th capillary area measure.
method Solving a Hessian-type equation with Robin boundary condition.
result Existence and uniqueness of a smooth solution under natural conditions.
We classify homothetical surfaces with constant mean curvature in hyperbolic space.
problem Classifying surfaces with constant mean curvature in hyperbolic space.
method Using the upper half-space model, we define surfaces by and prove they are parabolic.
result All homothetical surfaces with constant mean curvature in hyperbolic space are parabolic.
A 3D catenoid in 4D space is a minimal hypersurface that cannot be extended to a higher-dimensional half-space.
problem Extending the half-space theorem to higher dimensions in .
method Analyzing the topological constraints on minimal hypersurfaces in .
result A complete, properly embedded minimal hypersurface in a slab in must be a hyperplane.
Paper solves capillary Orlicz-Minkowski problem with new inequalities.
problem Finding capillary convex bodies with prescribed Orlicz surface area measures.
method Continuity method and inequalities to solve the capillary even Orlicz-Minkowski problem.
result Volume-normalized smooth solutions and inequalities established.
The Margulis constant for Kleinian groups is the smallest constant such that for each discrete group and each point in the upper half space , the group generated by the elements in which move less than distance c is elementary. We take a first step towards determining this constant by p…
New proofs and inequalities for capillarity problems quantify asymmetries.
problem Quantifying asymmetries in capillarity functionals.
method ABP-type technique, symmetrization, selection-type argument.
result Sharp quantitative inequalities for asymmetries in capillarity problems.
A new screening test for Lasso improves solution speed.
problem Improving the efficiency of Lasso solution methods.
method Safe region with dome geometry based on dual cutting half-spaces.
result The new screening test leads to significant acceleration.
Develops a method to prove Penrose inequality for half-spaces.
problem Proving the Riemannian Penrose inequality for asymptotically flat half-spaces.
method Doubling procedure for asymptotically flat half-spaces with non-negative scalar curvature and mean-convex boundary.
result Obtains the Penrose-type inequality for dimensions 3 to 7.
Classification of solutions to the -flat and constant -curvature equation on the half-space and ballmath.AP
Study classifies solutions to specific equations on half-space and ball.
problem Classifying nonnegative solutions to -flat and constant -curvature equations.
method Introduced a biharmonic Poisson kernel and derived its explicit representation formula.
result Established classification theorems for solutions on and .
The paper proves nonexistence results for translating solitons in r-mean curvature flow.
problem Proving nonexistence of translating solitons in r-mean curvature flow.
method Establishing nonexistence results under suitable growth conditions on curvature and second fundamental form.
result Properly immersed translating solitons cannot be confined to certain half-spaces.
The paper constructs homotopically non-trivial spheres in complexified spaces.
problem Embedding spheres in complexified spaces defined by hyperplane arrangements.
method Introducing locally consistent systems of half-spaces, embedding a sphere, and computing twisted intersection numbers.
result The constructed sphere is homotopically non-trivial if the half-space system is globally consistent.
Equations of motion for linear Hamiltonians in the real Jacobi group
problem Equations of motion for linear Hamiltonians in the real Jacobi group
method Using the energy function on the extended Siegel-Jacobi upper half space
result Equations of motion attached to linear Hamiltonians in the generators of the real Jacobi group
We study a half-space problem related to graphs in , where is the hyperbolic plane, having constant mean curvature defined over unbounded domains in .