Displaying similar documents to “Hardy inequalities in strips on ruled surfaces.”

Spectrum of the laplacian in a narrow curved strip with combined Dirichlet and Neumann boundary conditions

David Krejčiřík (2009)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

We consider the laplacian in a domain squeezed between two parallel curves in the plane, subject to Dirichlet boundary conditions on one of the curves and Neumann boundary conditions on the other. We derive two-term asymptotics for eigenvalues in the limit when the distance between the curves tends to zero. The asymptotics are uniform and local in the sense that the coefficients depend only on the extremal points where the ratio of the curvature radii of the Neumann boundary to the Dirichlet...

The PDE describing constant mean curvature surfaces

Hongyou Wu (2001)

Mathematica Bohemica

Similarity:

We give an expository account of a Weierstrass type representation of the non-zero constant mean curvature surfaces in space and discuss the meaning of the representation from the point of view of partial differential equations.

On the Regularity of Alexandrov Surfaces with Curvature Bounded Below

Luigi Ambrosio, Jérôme Bertrand (2016)

Analysis and Geometry in Metric Spaces

Similarity:

In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.

Invariants and Bonnet-type theorem for surfaces in ℝ4

Georgi Ganchev, Velichka Milousheva (2010)

Open Mathematics

Similarity:

In the tangent plane at any point of a surface in the four-dimensional Euclidean space we consider an invariant linear map ofWeingarten-type and find a geometrically determined moving frame field. Writing derivative formulas of Frenet-type for this frame field, we obtain eight invariant functions. We prove a fundamental theorem of Bonnet-type, stating that these eight invariants under some natural conditions determine the surface up to a motion. We show that the basic geometric classes...

Isospectral Riemann surfaces

Peter Buser (1986)

Annales de l'institut Fourier

Similarity:

We construct new examples of compact Riemann surfaces which are non isometric but have the same spectrum of the Laplacian. Examples are given for genus g = 5 and for all g ≥ 7 . In a second part we give examples of isospectral non isometric surfaces in R 3 which are realizable by paper models.