Dr Wilhelm Klingenberg's Outputs (34)

A capillary problem for spacelike mean curvature flow in a cone of Minkowski space (2024)
Journal Article
Klingenberg, W., Lambert, B., & Scheuer, J. (2025). A capillary problem for spacelike mean curvature flow in a cone of Minkowski space. Journal of Evolution Equations, 25(1), Article 15. https://doi.org/10.1007/s00028-024-01045-7

Consider a convex cone in three-dimensional Minkowski space which either contains the light cone or is contained in it. This work considers mean curvature flow of a proper spacelike strictly mean convex disc in the cone which is graphical with respec... Read More about A capillary problem for spacelike mean curvature flow in a cone of Minkowski space.

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

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-y

We 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.2022.320.1

We 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/s42985-021-00128-1

In 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/s0008439520000910

We 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.1639

We 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), 455-467

A 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/7766

We 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/s1446788717000210

We 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.

A Converging Lagrangian Flow in the Space of Oriented Line (2016)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2016). A Converging Lagrangian Flow in the Space of Oriented Line. Kyushu journal of mathematics, 70(2), 343-351. https://doi.org/10.2206/kyushujm.70.343

Under mean radius of curvature flow, a closed convex surface in Euclidean space is known to expand exponentially to infinity. In the three-dimensional case we prove that the oriented normals to the flowing surface converge to the oriented normals of... Read More about A Converging Lagrangian Flow in the Space of Oriented Line.

Erratum to: On the geometry of the space of oriented geodesicd (2016)
Journal Article
Alekseevsky, D., Guilfoyle, B., & Klingenberg, W. (2016). Erratum to: On the geometry of the space of oriented geodesicd. Annals of Global Analysis and Geometry, 50, 97–99. https://doi.org/10.1007/s10455-016-9515-3

Totally null surfaces in neutral Kähler 4-manifolds (2016)
Journal Article
Georgiou, N., Guilfoyle, B., & Klingenberg, W. (2016). Totally null surfaces in neutral Kähler 4-manifolds. Balkan Journal of Geometry and its Applications, 21(1), 27-41

We study the totally null surfaces of the neutral Kähler metric on certain 4-manifolds. The tangent spaces of totally null surfaces are either self-dual (α-planes) or anti-self-dual (β-planes) and so we consider α-surfaces and β-surfaces. The metric... Read More about Totally null surfaces in neutral Kähler 4-manifolds.

On the geometry of spaces of oriented geodesics. (2011)
Journal Article
Alekseevsky, D., Guilfoyle, B., & Klingenberg, W. (2011). On the geometry of spaces of oriented geodesics. Annals of Global Analysis and Geometry, 40(4), 389-409. https://doi.org/10.1007/s10455-011-9261-5

Let M be either a simply connected pseudo-Riemannian space of constant curvature or a rank one Riemannian symmetric space, and consider the space L(M) of oriented geodesics of M. The space L(M) is a smooth homogeneous manifold and in this paper we de... Read More about On the geometry of spaces of oriented geodesics..

On Weingarten surfaces in Euclidean and Lorentzian 3-space (2010)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2010). On Weingarten surfaces in Euclidean and Lorentzian 3-space. Differential Geometry and its Applications, 28(4), 454-468. https://doi.org/10.1016/j.difgeo.2009.12.002

We study the neutral Kähler metric on the space of time-like lines in Lorentzian View the MathML source, which we identify with the total space of the tangent bundle to the hyperbolic plane. We find all of the infinitesimal isometries of this metric,... Read More about On Weingarten surfaces in Euclidean and Lorentzian 3-space.

Geodesic flow on the normal congruence of a minimal surface. (2009)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2009). Geodesic flow on the normal congruence of a minimal surface

On C2-smooth Surfaces of Constant Width. (2009)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2009). On C2-smooth Surfaces of Constant Width. Tbilisi Mathematical Journal, 2, 1-17

In this paper, we obtain a number of results for C2-smooth surfaces of constant width in Euclidean 3-space E3-. In particular, we establish an integral inequality for constant width surfaces. This is used to prove that the ratio of volume to cubed wi... Read More about On C2-smooth Surfaces of Constant Width..

Area-stationary surfaces in neutral Kähler 4-manifolds (2008)
Journal Article
Guilfoyle, B., & Klingenberg, W. (2008). Area-stationary surfaces in neutral Kähler 4-manifolds. Contributions to Algebra and Geometry, 49(2), 481-490

A neutral Kähler surface with applications in geometric optics. (2008)
Book Chapter
Guilfoyle, B., & Klingenberg, W. (2008). A neutral Kähler surface with applications in geometric optics. In D. V. Alekseevsky, & H. Baum (Eds.), Recent Developments in Pseudo-Riemannian Geometry (149-178). European Mathematical Society. https://doi.org/10.4171/051-1/5

The space L of oriented lines, or rays, in Euclidean 3-space E3 is a 4-dimensional space with an abundance of natural geometric structure. In particular, it boasts a neutral Kähler metric which is closely related to the Euclidean metric on E3. In thi... Read More about A neutral Kähler surface with applications in geometric optics..