- Nov 2023
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www.browndailyherald.com www.browndailyherald.com
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- Jul 2020
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Metternich, N. W. (2020). Drawback before the wave?: Protest decline during the Covid-19 pandemic. https://doi.org/10.31235/osf.io/3ej72
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www.cypherpunks.ca www.cypherpunks.ca
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6.6 Conjecture: TextSecure Iron Triangle
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- Apr 2018
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arxiv.org arxiv.org
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the scalar curvatureRofds2is given byR= (1−u−2)Rρ+u−2n−1∑i,jR0ijij+ 2n−1∑i=1Rnini= (1−u−2)Rρ+u−2R0−2u−1∆ρu+ 2u−3∂u∂ρH0whereR0is the scalar curvature ofNwith respect tods20andRρis the scalar curvatureof Σρwith the induced metric.
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- Sep 2017
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arxiv.org arxiv.org
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Let Σ0be a compact strictly convex hypersurface inRn,Xbe the position vector ofa point on Σ0, and letNbe the unit outward normal of Σ0atX. Let Σrbe the convexhypersurface described byY=X+rN, withr≥0. The Euclidean space outside Σ0canbe represented by(Σ0×(0,∞),dr2+gr)wheregris the induced metric on Σr. Consider the following initial value problem(2.1)2H0∂u∂r= 2u2∆ru+ (u−u3)Rron Σ0×[0,∞)u(x,0) =u0(x)whereu0(x)>0 is a smooth function on Σ0,H0andRrare the mean curvature and scalarcurvature of Σrrespectively, and ∆ris the Laplacian operator on Σr.
Note que de agora em diante o autor se detém a estudar esse caso particular, onde estão inteiramente determinadas as geometrias intrínseca e extrínseca das folhas do semi cilindro, obtido folheando-se pelas paralelas o exterior da hipersuperfície estritamente convexa dada a priori.
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Given a functionRonN, we want to find the equation forusuch that(1.2)ds2=u2dρ2+gρhas scalar curvatureR.
O papel da aplicação \( u: N \longrightarrow \mathbb{R} \) é distorcer as fibras do semi cilindro \( N \), por dilatações e torções, deixando a geometria intrínseca das folhas invariante, de tal forma que o resultado seja um semi cilindro com a curvatura escalar prescrita \( \mathcal{R} \).
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Let Σ be a smooth compact manifold without boundary with dimensionn−1 and letN= [a,∞)×Σ equipped with a Riemannian metric of the form(1.1)ds20=dρ2+gρfor a point (ρ,x)∈N. Heregρis the induced metric on Σρwhich is the level surfaceρ=constant
Isso significa que a construção a seguir é feita a partir de um semi cilindro em que a geometria das folhas é dada a priori.
Esse artigo não trata da construção desse semi cilindro inicial.
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- Dec 2015
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arxiv.org arxiv.org
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Lemma 2.3.(2.1) has a unique solutionufor allrwhich satisfies the estimates in Lemma2.2.
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Let Σ0be a smooth compact strictly convex hypersurface inRn. Letrbe the distance function from Σ0. Then the metric on the exteriorNof Σ0is given bydr2+gr, wheregris the induced metric on Σr, which is the hypersurface with distancerfrom Σ0. The functionuwith prescribed scalar curvatureR= 0 is given by2H0∂u∂r= 2u2∆ru+ (u−u3)RrwhereH0is the mean curvature of Σr,Rris the scalar curvature of ΣrandR0is the scalarcurvature of Σrwith the induced metric fromRnand ∆ris the Laplacian on Σr.
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- May 2015
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oxfordstudent.com oxfordstudent.com
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eccentricities of Grigori Perelman
What eccentricities? He just lives with his parents and did not accept either the Fields' Medal or the Claymath's Millennium Prize.
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