Paper solves Minkowski problem for non-compact convex sets with asymptotic boundary conditions.
problem Solving Minkowski problem for non-compact convex sets with asymptotic boundary conditions.
method Combining covolume, Hadamard variational formula, and geometric interpretation.
result Solved Minkowski problem for non-compact convex sets under asymptotic conditions.
New examples of isoparametric families on non-compact symmetric spaces.
problem Constructing isoparametric families with non-austere focal sets.
method New extension method from Euclidean spaces to symmetric spaces of non-compact type.
result First examples of isoparametric families on non-compact symmetric spaces.
Paper proves non-compact inaudibility of symmetry and commutativity.
problem Proving inaudibility of symmetry and commutativity in non-compact settings.
method Using isospectral pairs of generalized Heisenberg groups.
result Proved inaudibility of weak symmetry and commutativity.
Proves well-posedness of the Cauchy problem for the Dirac operator on non-compact spacetimes.
problem Proving well-posedness of the Cauchy problem for the Dirac operator on non-compact spacetimes.
method Analyzes globally hyperbolic manifolds with complete spacelike Cauchy hypersurfaces.
result Proves well-posedness of the Cauchy problem for the Dirac operator.
This paper shows stable mappings are never dense on non-compact manifolds.
problem Density of stable mappings on non-compact manifolds.
method Complementing Mather's theory, proving stability results for non-compact manifolds.
result The set of stable mappings is never dense on non-compact manifolds.
Let F be a foliation of codimension 2 on a compact manifold with at least one non-compact leaf. We show that then F must contain uncountably many non-compact leaves. We prove the same statement for oriented p-dimensional foliations of arbitrary codimension if there exists a closed p form which evaluates positively on e…
Paper proves geodesic ball maximizes second Robin eigenvalue in non-compact symmetric spaces.
problem Maximizing the second Robin eigenvalue in non-compact rank-1 symmetric spaces.
method Quantitative spectral inequality for the second Robin eigenvalue.
result Geodesic ball maximizes the second Robin eigenvalue among domains of the same volume.
The paper proves strong holomorphic Morse inequalities on complex manifolds with optimal estimates.
problem Holomorphic Morse inequalities on non-compact complex manifolds with optimal fundamental estimates.
method Established strong holomorphic Morse inequalities under optimal fundamental estimates.
result Strong holomorphic Morse inequalities hold true on non-compact complex manifolds with optimal fundamental estimates.
In this note, we prove that the holonomy map from the set of equivalence classes of projective structures of parabolic type on non compact surfaces to the set of equivalence classes of parabolic representations of the fundamental group of the surface to P SL 2 (C) is a local biholomorphism.
Study shows unique harmonic metrics for certain Higgs bundles over non-compact surfaces.
problem Finding harmonic metrics for specific Higgs bundles.
method Generalized Kalka-Yang's theorem for non-compact hyperbolic surfaces to a coupled system.
result Generically regular nilpotent Higgs bundles admit unique maximal harmonic metrics.
Non-compact manifolds prevent C0-stable mappings from being dense.
problem Density of C0-stable mappings on non-compact manifolds. method Using topologically critical points to show non-density.
result The set of C0-stable mappings is never dense on non-compact manifolds. The paper studies rigidity results for harmonic forms on Kähler manifolds.
problem Understanding harmonic forms on Kähler manifolds.
method Analyzes rigidity results for harmonic (p,q)-forms in complete Kähler manifolds. result Shows several rigidity results and applications to non-compact Kähler manifolds.
Study harmonic metrics on Higgs bundles on non-compact Riemann surfaces.
problem Proving the existence and uniqueness of harmonic metrics on Higgs bundles.
method Analyzing Higgs bundles equipped with a non-degenerate symmetric pairing on non-compact Riemann surfaces.
result Proving the existence and uniqueness of compatible harmonic metrics under certain conditions.
Extends Atiyah-Singer Dirac operator study to non-compact spacetimes.
problem Analyzing Dirac operator on non-compact spacetimes with non-compact Cauchy hypersurface.
method Building on previous works, extends Fredholm result to non-compact Lorentzian spaces, using von Neumann algebras and Galois coverings.
result Γ-Fredholmness of the Dirac operator under APS boundary conditions.
New criterion found for Hermitian-Yang-Mills metrics on non-compact Kähler manifolds.
problem Existence of Hermitian-Yang-Mills metrics on non-compact Kähler manifolds.
method Algebraic criterion and stability condition introduced.
result New stability condition is both sufficient and necessary for the existence of Hermitian-Yang-Mills metrics.
We give a formulation of a deformation of Dirac operator along orbits of a group action on a possibly non-compact manifold to get an equivariant index and a K-homology cycle representing the index. We apply this framework to non-compact Hamiltonian torus manifolds to define geometric quantization from the view point of…
The paper studies how certain surfaces evolve in space-time.
problem Preserving the space-like condition of non-compact hypersurfaces.
method Prescribed mean curvature flow in generalized Robertson-Walker spaces.
result The flow preserves space-like condition and exists for infinite time.
In this work we prove the existence of embedded closed minimal hypersurfaces in non-compact manifolds containing a bounded open subset with smooth and strictly mean-concave boundary and a natural behavior on the geometry at infinity. For doing this, we develop a modified min-max theory for the area functional following…
Study on diffeotopy groups of non-compact 4-manifolds, extending previous results.
problem Understanding diffeotopy groups of non-compact 4-manifolds.
method Analyzing smoothings of punctured 4-manifolds and proving properties of diffeotopy groups.
result Uncountable diffeotopy groups for certain non-compact 4-manifolds.
Researchers derived heat kernel expansions for non-compact spaces using Witten deformation.
problem Heat kernel expansions on non-compact spaces, especially for Witten Laplacians.
method Introduced parabolic distance and used it to derive asymptotic expansions.
result Derived an asymptotic expansion of trace of heat kernel for small-time t. We classify Veech groups of tame non-compact flat surfaces. In particular we prove that all countable subgroups of GL+(2,R) avoiding the set of mappings of norm less than 1 appear as Veech groups of tame non-compact flat surfaces which are Loch Ness monsters. Conversely, a Veech group of any tame flat surf…
Researchers prove positive mass theorem for manifolds with arbitrary ends.
problem Proving the positive mass theorem for manifolds with non-compact ends.
method Developed techniques to handle non-compact singular sets and used Wloc1,p metrics. result Established positive mass theorem for C0 arbitrary ends with Wloc1,p metrics. This work extends PAC-Bayesian learning guarantees to non-compact symmetries and non-invariant data.
problem Lack of theoretical guarantees explaining the benefits of symmetries in machine learning models.
method Adapting and tightening PAC-Bayes bounds for non-compact symmetries and non-invariant data distributions.
result Theoretical evidence that symmetric models are preferable for symmetric data, beyond compact groups and invariant distributions.
We show that a group of diffeomorphisms $\D$ on the open unit interval I, equipped with the topology of uniform convergence on any compact set of the derivatives at any order, is non regular: the exponential map is not defined for some path of the Lie algebra. this result extends to the group of diffeomorphisms of fi…
Classifies π1-injective maps between non-compact surfaces.
problem Characterizing maps with injective fundamental groups.
method Proper homotopy classification of maps.
result All π1-injective proper maps are classified. The study extends conserved quantities theory to non-compact boundary initial data sets.
problem Extending conserved quantities theory to initial data sets with non-compact boundaries.
method Analysis of scalar curvature and mean curvature in the interior and boundary.
result Rigidity/flexibility phenomena in positive mass theorems and Penrose inequalities.
New non-existence results for harmonic maps into perturbed cones.
problem Proper harmonic maps into perturbed cones in \(\mathbb{R}^n\), horospheres in \(\mathbb{H}^n\).
method Extension of foliated maximum principle to non-compact settings.
result New non-existence results for proper harmonic maps.
Abreu-Sena-Dias have constructed two distinct families of scalar-flat Kähler non-compact toric metrics using Donaldson's rephrasing of Joyce's construction in action-angle coordinates. In this paper and using the same set-up, we show that these are the only J-complete scalar-flat Kähler metrics on any given strictly un…
The topological type of a non-compact Riemann surface is determined by its ends space and the ends having infinite genus. In this paper for a non-compact Riemann Surface Sm,s with s ends and exactly m of them with infinite genus, such that m,s∈N and 1<m≤s, we give a precise description of t…
Study Szegő kernel on non-compact CR manifolds with specific conditions.
problem Analyzing Szegő kernel on non-compact CR manifolds.
method Establish Szegő kernel asymptotic expansions on non-compact strictly pseudoconvex CR manifolds with transversal CR R-action under natural geometric conditions. result Szegő kernel asymptotic expansions established on non-compact CR manifolds.
Closed geodesics found on specific non-compact manifolds.
problem Existence of closed geodesics on non-compact Riemannian manifolds.
method Conditions on the manifold and its boundary to ensure the existence of closed geodesics.
result Existence of non-trivial closed geodesics on the manifold.
Develops quantization for non-compact complex manifolds with spectral gap.
problem Quantization of non-compact complex manifolds with spectral gap.
method Berezin-Toeplitz quantization, spectral gap analysis, asymptotic expansion.
result Toeplitz operators form a closed algebra and satisfy a complete composition expansion.
Non-compact convex sets in hyperbolic 3-space are rigid under isometries.
problem Rigidity of non-compact convex sets in hyperbolic 3-space
method Proving rigidity using Pogorelov's theorem and properties of locally convex surfaces
result Any intrinsic isometry between the boundaries of two non-compact closed convex subsets extends to a global isometry of the ambient space
Sharp lower bound for p-Laplacian eigenvalue on non-compact manifolds.
problem Estimating eigenvalues of p-Laplacian on non-compact manifolds. method Sharp lower bound established through domain properties and curvature conditions.
result Sharp lower bound for the first Dirichlet eigenvalue of p-Laplacian. The paper develops new methods to study sharp isoperimetric properties on complex spaces.
problem Sharp isoperimetric comparison on non-collapsed spaces with lower Ricci bounds.
method Original argument to estimate first and second variation of the area for isoperimetric sets, avoiding regularity theory.
result Generalizes results for smooth and non-compact manifolds, Alexandrov spaces, and convex bodies.
Strong rigidity proven for non-compact surfaces.
problem Proving rigidity of non-compact surfaces.
method Generalized result showing proper homotopy to homeomorphism.
result All non-compact orientable surfaces, except plane and punctured plane, are topologically rigid.
In this paper, we prove a functorial aspect of the formal geometric quantization procedure of non-compact spin-c manifolds.
The paper finds infinitely many magnetic geodesics on non-compact manifolds.
problem Existence and multiplicity of periodic orbits of magnetic flows.
method Morse theory applied to non-compact manifolds with energy levels above the Mañé critical value.
result Infinitely many noncontractible closed magnetic geodesics found.
Paper calculates homotopy types of non-compact surfaces using groupoids.
problem Computing homotopy types of non-compact foliated surfaces.
method Application of van Kampen theorem for groupoids.
result Computation of homotopy types for specific non-compact surfaces.
Extends soliton theory to non-compact cases.
problem Generalized solitons in non-compact settings.
method Place conditions on vector field and curvature, use tensor properties.
result Non-compact q-solitons are stationary and q-flat. Study finds solutions for complex problems on non-compact manifolds.
problem Solving fully nonlinear Yamabe-type problems on non-compact manifolds.
method Existence results for a class of problems, considering both positive and negative cases.
result Explicit examples of manifolds satisfying the hypotheses of the theorems.
Study eta invariant on non-compact manifolds with positive scalar curvature.
problem Proving geometric formulas and index theorems for uniformly positive scalar curvature metrics.
method Using Dirac-Schrödinger operators and relative eta invariant.
result New geometric formula for spectral flow and index formula for uniformly positive scalar curvature metrics.
Let D be a (generalized) Dirac operator on a non-compact complete Riemannian manifold M acted on by a compact Lie group G. Let v:M−−>Lie(G) be an equivariant map, such that the corresponding vector field on M does not vanish outside of a compact subset. These data define an element of K-theory of the tran…
We give a proof of the cobordism invariance of the index of elliptic pseudodifferential operators on sigma-compact manifolds, where, in the non-compact case, the operators are assumed to be multiplication outside a compact set. We show that, if the principal symbol class of such an elliptic operator on the boundary of …
Positive mass theorem for non-smooth metrics on flat manifolds with corners.
problem Proving a positive mass theorem for non-smooth metrics on asymptotically flat manifolds with non-compact boundary.
method Proves a positive mass theorem for metrics that are only continuous across a compact hypersurface.
result Obtains a positive mass theorem on manifolds with non-compact corners.
The paper studies HKKN stratifications for non-compact spaces and proves convexity properties.
problem Proving convexity properties of moment maps for non-compact subsets.
method Algebraic and analytical study of HKKN stratifications for a vector space and compact Kähler manifold, then applying to non-compact subsets.
result Convexity properties of moment maps for invariant subsets are proven.
Paper proves eigenvalue inequality for Hopf-symmetric domains.
problem Eigenvalue inequality for Hopf-symmetric domains in non-compact symmetric spaces.
method Used geometric and spectral analysis on non-compact rank one symmetric spaces.
result Eigenvalue inequality for bounded Hopf-symmetric domains in non-compact symmetric spaces.
Compact curve solution emerges from non-compact curve.
problem Constructing solutions from non-compact curves.
method Slingshot solution to curve shortening flow.
result Compact embedded solution exists for a finite time.