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Reassessing the Strength of a Class of Wigner's Friend No-Go Theorems. [PDF]

Entropy (Basel)
Okon E.
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Modeling and Tracking of Maneuvering Extended Object With Random Hypersurface

IEEE Sensors Journal, 2021
Extended object tracking, an important and emerging research field, has attracted attention for applications in civilian and military fields. However, the modeling and tracking of maneuvering extended objects still face challenges that need to be solved ...
Lifan Sun, Haofang Yu, Zhumu Fu, Zishu He, Jie Zou   +4 more
semanticscholar   +1 more source

Hypersurface Data: General Properties and Birkhoff Theorem in Spherical Symmetry

Mediterranean Journal of Mathematics, 2020
The notions of (metric) hypersurface data were introduced in Mars (Gen Relativ Gravit 45:2175–2221, 2013) as a tool to analyze, from an abstract viewpoint, hypersurfaces of arbitrary signature in pseudo-Riemannian manifolds.
M. Mars
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A Lower Bound for the Determinantal Complexity of a Hypersurface

Foundations of Computational Mathematics, 2015
We prove that the determinantal complexity of a hypersurface of degree $$d > 2$$d>2 is bounded below by one more than the codimension of the singular locus, provided that this codimension is at least 5.
J. Alper, Tristram C. Bogart, Mauricio Velasco   +2 more
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Polynomial Partitioning on Varieties of Codimension Two and Point-Hypersurface Incidences in Four Dimensions

Discrete & Computational Geometry, 2014
We present a polynomial partitioning theorem for finite sets of points in the real locus of an irreducible complex algebraic variety of codimension at most two.
S. Basu, M. Sombra
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On the Fukaya category of a Fano hypersurface in projective space

Publications mathématiques (Bures-sur-Yvette), 2013
This paper is about the Fukaya category of a Fano hypersurface X⊂CPn$X \subset \mathbf {CP}^{n}$. Because these symplectic manifolds are monotone, both the analysis and the algebra involved in the definition of the Fukaya category simplify considerably ...
Nick Sheridan
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The Convex Hull of a Hypersurface

Proceedings of the London Mathematical Society, 1985
Given a codimension 1 smooth immersed submanifold \(M^ m\) in \(E^{m+1}\), the authors study the structure of the frontier H(f) of the convex hull of the image of \(M^ m\) in \(E^{m+1}\). First of all, they show that there exists a star-shaped smooth embedding h of the m-sphere \(S^ m\) into \(E^{m+1}\) with \(H(h)=H(f)\). Using this, a panel structure
Robertson, S. A., Romero-Fuster, M. C.
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Brownian Motion on a Hypersurface

Bulletin of the London Mathematical Society, 1985
Let \(f:R^ d\to R\) be a \(C^ 2\) function and let \(V=f^{-1}(c)\) be a level surface on which grad f(x) is never zero and orient V with the field n(\(\cdot)\) of normal vectors. Let H(x) be the mean curvature at x. We prove the following: 1. A process X in \(R^ d\) with \(f(X_ 0)=c\) and \(dX=dB n(X)+2^{-1}(d- 1)H(X)n(X)dt\) is a Brownian motion on ...
van den Berg, M., Lewis, J. T.
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Hypersurfaces with Congruent Geodesics

Mathematische Nachrichten, 1992
It is the purpose of this paper to prove the following theorem: Let \(M\) be a compact hypersurface of a complete, simply connected space \(N\) of constant curvature, and suppose that all geodesics of \(M\) are congruent in \(N\). Then \(M\) is an extrinsic sphere of positive curvature. The article contains many nice geometric ideas.
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On a Variational Problem on Hypersurfaces

Journal of the London Mathematical Society, 1973
\«\dV £ cm, (1) M where cm denotes the area of a unit m-sphere. The equality sign of (1) holds when and only when M is a hypersphere in E. In order to know whether the inequality (1) can be improved for some given hypersurfaces in E, it is important to know the S-hypersurfaces in E, i.e., the stable hypersurfaces in E with respect to the integral ot ...
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