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Topic: Hypersurfaces

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	Interactive Architecture dot Org » Systems of Exchange, Stephen Perrella, Hypersurfaces
		Stephen Perrella’s hypersurface is a realitively new theory of liquid-embodied architecture to displace the nostalgia and re-realization being carried into the spatial conceptions of new-media technology.
		“Hypersurfaces is the word we are using to describe any set of relationships that behave as systems of exchange.”
		Would be happy to re connect on these issues in reference to banal use of BMS in contemporary built environment.
	www.interactivearchitecture.org /systems-of-exchange-stephen-perrella-hypersurfaces.html (280 words)

	leuschke.org :: Research/Hypersurfaces of Bounded Cohen-Macaulay Type
		This is the first of a pair of papers that I wrote with Roger Wiegand in 2002.
		There were two particularly fun parts: the general construction that shows that every hypersurface of bounded Cohen-Macaulay type comes from one of dimension one, and the delicate calculations that rule out most candidates in dimension one.
		Roger and I passed this manuscript back and forth by email for months (changing it from LaTeX to AMSTeX and back again each time).
	www.leuschke.org /Research/HypersurfacesOfBoundedCohen-MacaulayType (266 words)

	2.4 Example: Minkowski space
		Furthermore, there are two hypersurfaces which intersect the time axis in the same two points as the asymptotically flat ones.
		This geometric statement about the behaviour of the hypersurfaces in the unphysical space-time translates back to the physical space-time as a statement about asymptotic fall-off conditions of the induced (physical) metric on the hypersurfaces, namely that asymptotically the metric has constant negative curvature.
		Also, in most numerical treatments of Einstein's equations the same method is used to evolve space-times from one space-like hypersurface to the next (see Section 4).
	relativity.livingreviews.org /Articles/lrr-2000-4/node6.html (1449 words)

	ACGRG Abstract (Site not responding. Last check: 2007-10-19)
		The existence of constant mean curvature (CMC) spacelike hypersurfaces in a variety of spacetimes has been proved by numerous authors (see [1],[2] for example).
		The form of MCF we use moves arbitrary smooth spacelike hypersurfaces in their normal direction at speed equal to the mean curvature minus a constant.
		MCF has been used previously to construct prescribed mean curvature hypersurfaces in cosmological spacetimes [3].
	www.maths.monash.edu.au /~leo/acgrg/acgrg4/html/abstracts/abstract02.html (183 words)

	2.4 Example: Minkowski space
		correspond to three-dimensional space-like hypersurfaces that are asymptotically Euclidean.
		Furthermore, there are two hypersurfaces that intersect the time axis in the same two points as the asymptotically flat ones.
		Even in Minkowski space-time we could choose space-like hypersurfaces that are not surfaces of constant Minkowski time but which nonetheless are asymptotically Euclidean.
	relativity.livingreviews.org /Articles/lrr-2004-1/articlesu4.html (1381 words)

	Alcubierre drive -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-19)
		There is no known way to induce such a wave, however, or to leave it once started; the Alcubierre drive remains a theoretical concept at this time.
		Using the 3+1 formalism of general relativity, the spacetime is described by a foliation of space-like hypersurfaces of constant coordinate time.
		where is the lapse function that gives the interval of proper time between nearby hypersurfaces, is the shift vector that relates the spatial coordinate systems on different hypersurfaces and is a positive definite metric on each of the hypersurfaces.
	www.absoluteastronomy.com /encyclopedia/a/al/alcubierre_drive.htm (878 words)

	Workshop on Harmonic Maps and Curvature Properties of Submanifolds, 2
		Abstract: A hypersurface M in Euclidean space or the sphere is said to be (proper) Dupin if the number g of distinct principal curvatures is constant on M, and if each principal curvature is constant along each leaf of its corresponding principal foliation.
		Important examples are the cyclides of Dupin and those hypersurfaces obtained from isoparametric hypersurfaces in a sphere by Lie sphere transformation.
		Abstract: The classification of Isoparametric hypersurfaces, Dupin hypersurfaces, developable hypersurfaces, etc. is an old and new problem, which is related to the Lie sphere geometry, projective geometry, and recently, to the theory of integrable systems.
	www.amsta.leeds.ac.uk /Pure/geometry/mabs.html (633 words)

	Fano Hypersurfaces in Weighted Projective 4-Spaces, Jennifer M. Johnson, János Kollár
		We also prove that many of these Fano hypersurfaces admit a Kähler-Einstein metric, and study the nonexistence of tigers on these Fano 3-folds.
		Finally, we prove that there are only finitely many families of quasismooth Calabi-Yau hypersurfaces in weighted projective spaces of any given dimension.
		This implies finiteness for various families of general type hypersurfaces.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.em/999188430 (194 words)

	Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry , Vol. 39, No. 2, pp. 395-411, ... (Site not responding. Last check: 2007-10-19)
		Abstract: The geometry of canal hypersurfaces of an $n$-dimensional conformal space $C^n$ is studied.
		Such hypersurfaces are envelopes of $r$-parameter families of hyperspheres, $1\leq r\leq n-2$.
		The main attention is given to the study of the Darboux maps of canal hypersurfaces in the de Sitter space $M_1^{n+1}$ and the projective space $P^{n+1}$.
	www.emis.de /journals/BAG/vol.39/no.2/15.html (148 words)

	Abstract: Deforming convex hypersurfaces by the nth root ... (Site not responding. Last check: 2007-10-19)
		Abstract: Deforming convex hypersurfaces by the nth root...
		In this paper we consider the deformation of convex hypersurfaces in euclidean space in the inward normal direction with speed equal to the nth root of the Gauss curvature.
		Huisken, who showed that the mean curvature flow shrinks convex hypersurfaces in euclidean space to round points, generalizing M. Gage and R.
	math.ucsd.edu /~benchow/minnhtml/research/nthroot.html (140 words)

	Citebase - On the Hodge Structure of Projective Hypersurfaces in Toric Varieties
		Authors: Batyrev, Victor V. Cox, David A. This paper generalizes classical results of Griffiths, Dolgachev and Steenbrink on the cohomology of hypersurfaces in weighted projective spaces.
		Given a d-dimensional projective simplicial toric variety P and an ample hypersurface X defined by an polynomial f in the homogeneous coordinate ring S of P (as defined in an earlier paper of the first author), we show that the graded pieces of the Hodge filtration on H
		Also, if T is the torus contained in X, then the intersection of X and T is an affine hypersurface in T, and we show how recent results of the second author can be stated using various ideals in the ring S.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:alg-geom/9306011 (1473 words)

	The Curvatures of Hypersurfaces (Site not responding. Last check: 2007-10-19)
		A hypersurface is an n-dimensional manifold embedded in an n+1 dimensional space. Common examples of hypersurfaces include one-dimensional plane curves, and two-dimensional surfaces in three-dimensional space. In higher-dimensional hypersurfaces the concept of principal curvatures can immediately be generalized to give a nice characterization of the overall curvature of the manifold.
		Since the first n coordinates are all tangent to the surface at the origin, the first partial derivatives of h with respect to these coordinates all vanish at the origin. Hence the lowest-order terms in the power series expansion of this function are second-order, so up to second order we have
		represent the n principal curvatures of the hypersurface at the point in question. These are simply the sectional one-dimensional curvatures in the n orthogonal directions. The determinant of c
	www.mathpages.com /home/kmath520/kmath520.htm (1154 words)

	Computer Science: Publication: Piecewise Linear Hypersurfaces using the Marching Cubes Algorithm
		Piecewise Linear Hypersurfaces using the Marching Cubes Algorithm
		Thus similarly, in four dimensions hypersurfaces may be formed around hyperobjects.
		These surfaces (or contours) are often formed from a set of connected triangles (or lines).
	www.cs.kent.ac.uk /pubs/1999/700 (304 words)

	Abstract: Deforming convex hypersurfaces by the square root ... (Site not responding. Last check: 2007-10-19)
		Abstract: Deforming convex hypersurfaces by the square root...
		In this paper we consider the deformation of convex hypersurfaces in euclidean space in the inward normal direction with speed equal to the square root of the scalar curvature.
		We show that for a class of initial convex hypersurfaces, a solution exists until the hypersurface shrinks to a round point.
	math.ucsd.edu /~benchow/minnhtml/research/sqrtscal.html (101 words)

	Abstract of Rigid Spherical Hypersurfaces (Site not responding. Last check: 2007-10-19)
		Abstract: We prove that the equations of zero CR-curvature in the case of rigid hypersurfaces lead to an overdetermined system of differential equations with holomorphic coefficients.
		We also show that such a system is equivalent to the sphericity conditions provided the hypersurface in consideration has nondegenerate Levi form.
		As an application of this characterisation we prove real-analyticity of rigid spherical hypersurfaces of a certain class.
	wwwmaths.anu.edu.au /research.reports/mrr/94.081 (75 words)

	Counting hypersurfaces with up to six double points (Site not responding. Last check: 2007-10-19)
		Counting hypersurfaces with up to six double points, by Israel Vainsencher
		We present exponential formulas for the number of hypersurfaces in a k-dimensional family displaying k ordinary double points for k<7.
		She was misled by the case of curves, where corrections came essentially from triple points; believing the analogy for higher dimension would be ipsis literi, hence not present at all due to a naive count of constants, ergo, corrections not needed.)
	www.math.uiuc.edu /~dan/Kleiman60/vainsencher.html (113 words)

	Sen No Sen :: OhmyNews International: Hypersurfaces :: December :: 2004 (Site not responding. Last check: 2007-10-19)
		The idea of “hypersurface” is taken from new-generation architect Stephen Perrella’s book “Hyper Surface Architecture.”
		in order to create true hypersurface, we must premise it on an “ubiquitous” environment in which people could access a network anywhere at anytime.
		In other words, just as the Internet gave birth to cyberspace, the ubiquitous environment shall inevitably give rise to hypersurface.
	sennosen.blogsome.com /2004/12/23/ohmynews-international-hypersurfaces (373 words)

	Citebase - Determinantal hypersurfaces
		Authors: Beauville, A. Let X be a smooth hypersurface in projective space.
		We discuss a number of applications for hypersurfaces of small dimension.
		We show that it is isomorphic to the blow-up of the intermediate jacobian J(X) of X along the Fano surface of X.
	citebase.eprints.org /cgi-bin/citations?archiveID=oai:arXiv.org:math/9910030 (1206 words)

	Computing Least Area Hypersurfaces Spanning Arbitrary Boundaries
		The numerical least area problem for oriented hypersurfaces seeks algorithms which approximate area-minimizing hypersurfaces spanning a given boundary in Euclidean n-dimensional space.
		(The mathematical model is valid for hypersurfaces of arbitrary Euclidean n-dimensional spaces.) There are no a priori restrictions on either the topological complexity of the given boundary or the topological type of the surfaces considered.
		As an example which illustrates the power of the method, the algorithm is applied to a boundary consisting of a pair of square-shaped linked curves.
	epubs.siam.org /sam-bin/dbq/article/27890 (181 words)

	AMCA: Hypersurfaces of finite geometric type by Francesco Mercuri (Site not responding. Last check: 2007-10-19)
		We introduce, based on the properties of complete minimal surfaces of finite total curvature, a new class of hypersurfaces of Euclidean spaces, the hypersurfaces of finite geometric type, which is a much wider class, even in dimension two.
		For example we give a characterization of even dimensional cathenoids as the minimal hypersurfaces, regular at infinity, whoseGauss-Kroneker curvature is zero only on "low dimensional subsets".
		The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Mathematical Conference Abstracts.
	at.yorku.ca /c/a/f/h/20.htm (161 words)

	Geometry of hypersurfaces and complete intersections (Site not responding. Last check: 2007-10-19)
		The method of proof suggested that some further ``rational''-like properties could be shown for these varieties.
		18] regarding cohomological connectivity of hypersurfaces generalizes earlier results of S.
		In a slightly different direction cohomological connectivity results for hypersurfaces of low degree have been shown by H. Esnault, M. Nori and V.
	www.imsc.ernet.in /~kapil/work/node9.html (217 words)

	Journal of the American Mathematical Society (Site not responding. Last check: 2007-10-19)
		Abstract: In this paper, we study a second order variational problem for locally convex hypersurfaces, which is the affine invariant analogue of the classical Plateau problem for minimal surfaces.
		We prove existence, regularity and uniqueness results for hypersurfaces maximizing affine area under appropriate boundary conditions.
		Keywords: Affine Plateau problem, affine maximal hypersurface, affine area functional, affine maximal surface equation, variational problem, second boundary value problem, a priori estimates, strict convexity, interior regularity, Bernstein Theorem, Monge-Amp\`{e}re measure, curvature measure, Gauss mapping, locally convex hypersurface, generalized Legendre transform
	80-www.ams.org.library.uor.edu /jams/2005-18-02/S0894-0347-05-00475-3/home.html (458 words)

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