Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry
(2023)
Journal Article
Borza, S., & Klingenberg, W. (2024). Local non-injectivity of the exponential map at critical points in sub-Riemannian geometry. Nonlinear Analysis: Theory, Methods and Applications, 239, Article 113421. https://doi.org/10.1016/j.na.2023.113421
Outputs (33)
Roots of Polynomials and Umbilics of Surfaces (2023)
Journal Article
Guilfoyle, D., & Klingenberg, W. (2023). Roots of Polynomials and Umbilics of Surfaces. Results in Mathematics, 78(6), https://doi.org/10.1007/s00025-023-02003-4
Regularity and Continuity properties of the sub-Riemannian exponential map (2023)
Journal Article
Borza, S., & Klingenberg, W. (2023). Regularity and Continuity properties of the sub-Riemannian exponential map. Journal of Dynamical and Control Systems, 29(4), 1385-1407. https://doi.org/10.1007/s10883-022-09624-yWe prove a version of Warner’s regularity and continuity properties for the sub-Riemannian exponential map. The regularity property is established by considering sub-Riemannian Jacobi fields while the continuity property follows from studying the Mas... Read More about Regularity and Continuity properties of the sub-Riemannian exponential map.
Weyl Estimates for spacelike hypersurfaces in de Sitter space (2022)
Journal Article
Ballesteros-Chavez, D., Klingenberg, W., & Lambert, B. (2022). Weyl Estimates for spacelike hypersurfaces in de Sitter space. Pacific journal of mathematics, 320(1), 1-11. https://doi.org/10.2140/pjm.2022.320.1We study the isometric spacelike embedding problem in scaled de Sitter space, and obtain Weyl-type estimates and the corresponding closedness in the space of embeddings.
Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows (2021)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2021). Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows. Partial Differential Equations and Applications, 2(6), Article 72. https://doi.org/10.1007/s42985-021-00128-1In the 1950’s Hopf gave examples of non-round convex 2-spheres in Euclidean 3-space with rotational symmetry that satisfy a linear relationship between their principal curvatures. In this paper, we investigate conditions under which evolving a smooth... Read More about Evolving to Non-round Weingarten Spheres: Integer Linear Hopf Flows.
Prescribed $k$ symmetric curvature hypersurfaces in de Sitter space (2020)
Journal Article
Ballesteros-Chávez, D., Klingenberg, W., & Lambert, B. (2021). Prescribed $k$ symmetric curvature hypersurfaces in de Sitter space. Canadian Mathematical Bulletin, 64(4), 886-901. https://doi.org/10.4153/s0008439520000910We prove the existence of compact spacelike hypersurfaces with prescribed k-curvature in de Sitter space, where the prescription function depends on both space and the tilt function.
Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces (2020)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2020). Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces. Annales de la Faculté des sciences de Toulouse (En ligne), 29(3), 565-576. https://doi.org/10.5802/afst.1639We study the space of holomorphic discs with boundary on a surface in a real 2-dimensional vector bundle over a compact 2-manifold. We prove that, if the ambient 4-manifold admits a fibre-preserving transitive holomorphic action, then a section with... Read More about Fredholm-regularity of holomorphic discs in plane bundles over compact surfaces.
A global version of a classical result of Joachimsthal (2019)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2019). A global version of a classical result of Joachimsthal. Houston journal of mathematics, 45(2), 455-467A classical result attributed to Joachimsthal in 1846 states that if two surfaces intersect with constant angle along a line of curvature of one surface, then the curve of intersection is also a line of curvature of the other surface. In this note we... Read More about A global version of a classical result of Joachimsthal.
Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension (2019)
Journal Article
Guilfoyle, B., & Klingenberg, K. (2019). Mean Curvature Flow of Compact Spacelike Submanifolds in Higher Codimension. Transactions of the American Mathematical Society, 372(9), 6263-6281. https://doi.org/10.1090/tran/7766We prove the longtime existence for mean curvature flow of a smooth n-dimensional spacelike submanifold of an (n + m)-dimensional manifold whose metric satisfies the timelike curvature condition.
Parabolic Classical Curvature Flows (2017)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2018). Parabolic Classical Curvature Flows. Journal of the Australian Mathematical Society, 104(3), 338-357. https://doi.org/10.1017/s1446788717000210We consider classical curvature flows: 1-parameter families of convex embeddings of the 2-sphere into Euclidean 3-space, which evolve by an arbitrary (nonhomogeneous) function of the radii of curvature (RoC). We determine conditions for parabolic flo... Read More about Parabolic Classical Curvature Flows.