共查询到20条相似文献,搜索用时 15 毫秒
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An implicit non-steady free boundary problem is transformed into a variational inequality, which is solved by means of a semi-discretization technique. 相似文献
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Lawrence E. Payne Margaret E. Rayner 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》1972,23(1):13-15
Summary An isoperimetric inequality is obtained which relates theL
1-andL
2-integrals of the first eigenfunction in the problem of the vibrating clamped membrane.
Zusammenfassung Für das Problem der eingespannten schwingenden Membran wird zwischen demL 1-und demL 2-Integral der ersten Eigenfunktion eine isoperimetrische Ungleichung hergeleitet.相似文献
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Let (ξ(s)) s?≥ 0 be a standard Brownian motion in d?≥ 1 dimensions and let (D s ) s ≥?0 be a collection of open sets in ${\mathbb{R}^d}$ . For each s, let B s be a ball centered at 0 with vol(B s ) =?vol(D s ). We show that ${\mathbb{E}[\rm {vol}(\cup_{s \leq t}(\xi(s) + D_s))] \geq \mathbb{E}[\rm {vol}(\cup_{s \leq t}(\xi(s) + B_s))]}$ , for all t. In particular, this implies that the expected volume of the Wiener sausage increases when a drift is added to the Brownian motion. 相似文献
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An isoperimetric inequality for the Heisenberg groups 总被引:2,自引:0,他引:2
D. Allcock 《Geometric And Functional Analysis》1998,8(2):219-233
We show that the Heisenberg groups of dimension five and higher, considered as Riemannian manifolds, satisfy a quadratic isoperimetric inequality. (This means
that each loop of length L bounds a disk of area ~ L
2.) This implies several important results about isoperimetric inequalities for discrete groups that act either on or on complex hyperbolic space, and provides interesting examples in geometric group theory. The proof consists of explicit
construction of a disk spanning each loop in .
Submitted: April 1997, Final version: November 1997 相似文献
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Farroni Fernando Greco Luigi Migliaccio Lucia Moscariello Gioconda 《Ricerche di matematica》2014,63(1):131-141
We study stability for an integral isoperimetric inequality. 相似文献
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Ricerche di Matematica - Given a positive lower semi-continuous density f on $$mathbb {R}^2$$ the weighted volume $$V_f:=fmathscr {L}^2$$ is defined on the $$mathscr {L}^2$$ -measurable sets in... 相似文献
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V. A. Zalgaller 《Journal of Mathematical Sciences》2007,140(4):511-527
It is proved that a regular tetrahedron has the maximal possible surface area among all tetrahedra having surface with unit
geodesic diameter. An independent proof of O’Rourke-Schevon’s theorem about polar points on a convex polyhedron is given.
A. D. Aleksandrov’s general problem on the area of a convex surface with fixed geodesic diameter is discussed. Bibliography:
4 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 329, 2005, pp. 28–55. 相似文献
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In this note we will present a stability property of the reverse isoperimetric inequality newly obtained in [S.L. Pan, H. Zhang, A reverse isoperimetric inequality for convex plane curves, Beiträge Algebra Geom. 48 (2007) 303-308], which states that if K is a convex domain in the plane with perimeter p(K) and area a(K), then one gets , where denotes the oriented area of the domain enclosed by the locus of curvature centers of the boundary curve ∂K, and the equality holds if and only if K is a circular disc. 相似文献
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Peter Topping 《manuscripta mathematica》1999,100(1):23-33
We prove a new isoperimetric inequality which relates the area of a multiply connected curved surface, its Euler characteristic,
the length of its boundary, and its Gaussian curvature.
Received: 31 July 1998 相似文献
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Mitsuru Uchiyama 《Proceedings of the American Mathematical Society》2001,129(11):3339-3344
For bounded non-negative operators and , Furuta showed
We will extend this as follows: implies
where is a harmonic mean of and . The idea of the proof comes from Jensen's inequality for an operator convex function by Hansen-Pedersen.
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Steven Heilman 《Random Structures and Algorithms》2020,56(1):154-168
We prove the endpoint case of a conjecture of Khot and Moshkovitz related to the unique games conjecture, less a small error. Let n ≥ 2. Suppose a subset Ω of n‐dimensional Euclidean space satisfies ?Ω = Ωc and Ω + v = Ωc (up to measure zero sets) for every standard basis vector . For any and for any q ≥ 1, let and let . For any x ∈ ?Ω, let N(x) denote the exterior normal vector at x such that ‖N(x)‖2 = 1. Let . Our main result shows that B has the smallest Gaussian surface area among all such subsets Ω, less a small error: In particular, Standard arguments extend these results to a corresponding weak inequality for noise stability. Removing the factor 6 × 10?9 would prove the endpoint case of the Khot‐Moshkovitz conjecture. Lastly, we prove a Euclidean analogue of the Khot and Moshkovitz conjecture. The full conjecture of Khot and Moshkovitz provides strong evidence for the truth of the unique games conjecture, a central conjecture in theoretical computer science that is closely related to the P versus NP problem. So, our results also provide evidence for the truth of the unique games conjecture. Nevertheless, this paper does not prove any case of the unique games conjecture. 相似文献
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Yngve Domar 《Arkiv f?r Matematik》1968,7(5):433-441
LetA andB be positive numbers andm andn positive integers,m. Then there is for complex valued functions φ onR with sufficient differentiability and boundedness properties a representation wherev 1 andv 2 are bounded Borel measures withv 1 absolutely continuous, such that there exists a function φ with ∣φ(n)∣ ?A and ∣φ∣ ?A onR and satisfying $$\varphi ^{(m)} (0) = A\int_R {\left| {d\nu _1 } \right|} + B\int_R {\left| {d\nu _2 } \right|} .$$ This result is formulated and proved in a general setting also applicable to derivatives of fractional order. Necessary and sufficient conditions are given in order that the measures and the optimal functions have the same essential properties as those which occur in the particular case stated above. 相似文献
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Albrecht Küster 《manuscripta mathematica》1985,53(3):255-259
This paper contains a sharp version of the well-known linear isoperimetric inequality for minimal surfacesX area(X)1/2oscillation(X)length(X).Supported by Sonderforschungsbereich 72 der Deutschen Forschungsgemeinschaft at Bonn University. 相似文献
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A purely analytic proof is given for an inequality that has as a direct consequence the two most important affine isoperimetric
inequalities of plane convex geometry: The Blaschke-Santaló inequality and the affine isoperimetric inequality of affine differential
geometry. 相似文献
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