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We give a classification of all linear natural operators transforming affinors on each n-dimensional manifold M into affinors on $T^{A} M$ , where $T^{A}$ is the product preserving bundle functor given by a Weil algebra A, under the condition that n ≥ 2.

Linear liftings of skew-symmetric tensor fields to Weil bundles

Jacek Dębecki (2005)

Czechoslovak Mathematical Journal

We define equivariant tensors for every non-negative integer $p$ and every Weil algebra $A$ and establish a one-to-one correspondence between the equivariant tensors and linear natural operators lifting skew-symmetric tensor fields of type $(p, 0)$ on an $n$ -dimensional manifold $M$ to tensor fields of type $(p, 0)$ on $T^{A} M$ if $1 \leq p \leq n$ . Moreover, we determine explicitly the equivariant tensors for the Weil algebras $𝔻_{k}^{r}$ , where $k$ and $r$ are non-negative integers.

Lineare invariante Gebilde in äquiformen Bewegungen der Räume endlicher Dimension

Josef Somer (1979)

Aplikace matematiky

Linearization and explicit solutions of the minimal surface equations.

Alexander G. Reznikov (1992)

Publicacions Matemàtiques

We show that the apparatus of support functions, usually used in convex surfaces theory, leads to the linear equation Δh + 2h = 0 describing locally germs of minimal surfaces. Here Δ is the Laplace-Beltrami operator on the standard two-dimensional sphere. It explains the existence of the sum operator of minimal surfaces, introduced recently. In 4-dimensional space the equation Δ h + 2h = 0 becomes inequality wherever the Gauss curvature of a minimal hypersurface is nonzero.

Lines of curvature, ridges and conformal invariants of hypersurfaces.

Romero-Fuster, M.C., Sanabria-Codesal, E. (2004)

Beiträge zur Algebra und Geometrie

Linien, Flächen und höhere Gebilde in mehrfach ausgedehnten Gausschen und Riemannschen Räumen

E. Schering (1873)

Nachrichten von der Königl. Gesellschaft der Wissenschaften und der Georg-Augusts-Universität zu Göttingen

Linked Darboux motions.

Röschel, Otto (1996)

Mathematica Pannonica

Local constraints on Einstein-Weyl geometries.

M.G. Eastwood, K.P. Tod (1997)

Journal für die reine und angewandte Mathematik

Local gradient estimates of $p$ -harmonic functions, $1 / H$ -flow, and an entropy formula

Brett Kotschwar, Lei Ni (2009)

Annales scientifiques de l'École Normale Supérieure

In the first part of this paper, we prove local interior and boundary gradient estimates for $p$ -harmonic functions on general Riemannian manifolds. With these estimates, following the strategy in recent work of R. Moser, we prove an existence theorem for weak solutions to the level set formulation of the $1 / H$ (inverse mean curvature) flow for hypersurfaces in ambient manifolds satisfying a sharp volume growth assumption. In the second part of this paper, we consider two parabolic analogues of the $p$ -harmonic...

Local isometric immersions of R2 into R4.

M. Dajczer, M. Do Carmo (1993)

Journal für die reine und angewandte Mathematik

Local monotonicity of Hausdorff measures restricted to curves in $ℝ^{n}$

Robert Černý (2009)

Commentationes Mathematicae Universitatis Carolinae

We give a sufficient condition for a curve $γ : ℝ \to ℝ^{n}$ to ensure that the $1$ -dimensional Hausdorff measure restricted to $γ$ is locally monotone.

Local monotonicity of Hausdorff measures restricted to real analytic curves

Robert Černý (2010)

Commentationes Mathematicae Universitatis Carolinae

We prove that the 1-dimensional Hausdorff measure restricted to a simple real analytic curve $γ : ℝ \to ℝ^{N}$ , $N \geq 2$ , is locally 1-monotone.

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Lightlike ruled surfaces in $ℝ_{1}^{4}$ .

Lignes de courbure de la surface $z = L cos y - L cos x$

Lignes de divergence pour les graphes à courbure moyenne constante

Limit sets of Kleinian groups and conformally flat Riemannian manifolds.

Linear liftings of affinors to Weil bundles