강하게 고립된 특이점의 비지속성 및 기하학적 응용 - 임의의 여차원에서의 일반적인 정칙성 결과
리만 다양체에 있는 정상 적분 n-배열체의 강하게 고립된 특이점은 일반적으로 지속되지 않으며, 이는 거의 둥근 4-구에서 클리포드 풋볼 및 샹 초구의 지속성에 대한 질문에 대한 답을 제공합니다.
Global Curvature Estimates for Star-Shaped Hypersurfaces in Warped Product Manifolds with Prescribed Curvature Equations
This research paper establishes global curvature estimates for a class of hypersurfaces in warped product manifolds, significantly advancing the understanding of solutions to prescribed curvature equations in geometric analysis.
Radius Estimates for Nearly Stable Constant Mean Curvature Hypersurfaces of Dimension 2, 3, and 4
This research paper presents radius estimates for nearly stable constant mean curvature (CMC) hypersurfaces immersed in Riemannian manifolds with specific conditions, generalizing previous results for stable CMC hypersurfaces.
Upper Bound for the L2-Norm of the Euler Class of Foliations on Closed Irreducible Riemannian 3-Manifolds
This paper establishes an upper bound for the L2-norm of the Euler class of codimension one foliations on closed irreducible Riemannian 3-manifolds, relating geometric properties like volume, curvature, and mean curvature to the topology of foliations.
Green Functions of GJMS Operators on Spheres and Their Rigidity Properties
This research paper derives explicit formulas for Green functions of GJMS operators (including fractional ones) on spheres, revealing their connection to extrinsic geometry and proving rigidity theorems that characterize spheres based on these Green function properties.
The Propagation of Singularities in Convex Hypersurfaces of Constant Curvature in Hyperbolic Space
Singularities in the boundary of constant curvature convex hypersurfaces in hyperbolic space propagate along entire faces of the convex hull of the singular set towards the boundary of the domain.
Best Lipschitz Maps, Measured Laminations, and Earthquakes in Hyperbolic Surfaces
This research paper explores the intricate relationship between best Lipschitz maps, measured laminations, and earthquakes in the context of hyperbolic surfaces, demonstrating a novel connection between these concepts through the lens of Lie algebra valued transverse measures.
Compactness of Fueter Sections in Charge 2 Monopole Bundles over 3-Manifolds
This research paper investigates the compactness of Fueter sections within charge 2 monopole bundles over 3-manifolds, revealing that unbounded sequences of these sections, when renormalized, converge to non-zero Z2-harmonic 1-forms.
Conformal Scalar-flat Metrics with Prescribed Boundary Mean Curvature: Resolving Open Cases and New Solvability Conditions
This mathematics research paper establishes new solvability conditions for finding a conformal metric with zero scalar curvature in a manifold and prescribed mean curvature on its boundary, addressing open cases from Escobar's work.
Smooth Approximations of Constant-Mean-Curvature Hypersurfaces Possessing Isolated Singularities
This research paper proves that a constant-mean-curvature (CMC) hypersurface with an isolated singularity can be locally approximated by a sequence of smooth CMC hypersurfaces, establishing a generic regularity result for the CMC Plateau problem.
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