Results 1 to 10 of about 5,840 (179)
Regular homotopy and total curvature [PDF]
, 2006 We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of ...
Ekholm, Tobias
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Configuration spaces and Vassiliev classes in any dimension [PDF]
, 2002 The real cohomology of the space of imbeddings of S^1 into R^n, n>3, is studied by using configuration space integrals. Nontrivial classes are explicitly constructed. As a by-product, we prove the nontriviality of certain cycles of imbeddings obtained by
Alberto S Cattaneo +16 more
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The rigidity of embedded constant mean curvature surfaces [PDF]
, 2007 We study the rigidity of complete, embedded constant mean curvature surfaces in R^3. Among other things, we prove that when such a surface has finite genus, then intrinsic isometries of the surface extend to isometries of R^3 or its isometry group ...
Meeks III, William H. +1 more
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Homology of spaces of regular loops in the sphere [PDF]
, 2009 In this paper we compute the singular homology of the space of immersions of the circle into the $n$-sphere. Equipped with Chas-Sullivan's loop product these homology groups are graded commutative algebras, we also compute these algebras. We enrich Morse
Borgne, Jean-Francois Le, Chataur, David
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Existence and Regularity of Spheres Minimising the Canham-Helfrich Energy
, 2020 We prove existence and regularity of minimisers for the Canham-Helfrich energy in the class of weak (possibly branched and bubbled) immersions of the $2$-sphere.
Mondino, Andrea, Scharrer, Christian
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, 2007 Let $\Sigma$ be a compact surface. We prove that the set of surface cubications modulo flips, up to isotopy, is in one-to-one correspondence with $\Z/2\Z\oplus H_1(\Sigma,\Z/2\Z)$.Comment: revised version ...
Funar, Louis
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Double point self-intersection surfaces of immersions
, 2000 A self-transverse immersion of a smooth manifold M^{k+2} in R^{2k+2} has a double point self-intersection set which is the image of an immersion of a smooth surface, the double point self-intersection surface.
Asadi-Golmankhaneh, Mohammad A. +1 more
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Cartan--Whitney Presentation, Non-smooth Analysis and Smoothability of Manifolds: On a theorem of Kondo--Tanaka [PDF]
, 1968 Using tools and results from geometric measure theory, we give a simple new proof of the main result (Theorem 1.3) in K. Kondo and M. Tanaka, Approximation of Lipschitz Maps via Immersions and Differentiable Exotic Sphere Theorems, \textit{Nonlinear Anal.
Li, Siran
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Partial Isometries of a Sub-Riemannian Manifold
, 2012 In this paper, we obtain the following generalisation of isometric $C^1$-immersion theorem of Nash and Kuiper. Let $M$ be a smooth manifold of dimension $m$ and $H$ a rank $k$ subbundle of the tangent bundle $TM$ with a Riemannian metric $g_H$.
Eliashberg Y. +3 more
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On a Liu--Yau type inequality for surfaces
, 2014 Let $\Omega$ be a compact and mean-convex domain with smooth boundary $\Sigma:=\partial\Omega$, in an initial data set $(M^3,g,K)$, which has no apparent horizon in its interior.
Hijazi, Oussama +2 more
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