On asymptotic volume of tori

1995 ◽  
Vol 5 (5) ◽  
pp. 800-808 ◽  
Author(s):  
D. Burago ◽  
S. Ivanov
Keyword(s):  
Asymptotic Volume

scholarly journals Locality estimation of parallel algorithm for distributed memory computers

2020 ◽  
Vol 64 (6) ◽  
pp. 647-656
Author(s):  
N. A. Likhoded ◽  
A. A. Tolstsikau
Keyword(s):  
Parallel Algorithm ◽  
High Performance ◽  
Distributed Memory ◽  
Data Communication ◽  
Usage Level ◽  
Performance Of Algorithm ◽  
Algorithm Implementation ◽  
Asymptotic Volume ◽  
Fast Access ◽  
Communication Operations

Locality is an algorithm characteristic describing a usage level of fast access memory. For example, in case of distributed memory computers we focus on memory of each computational node. To achieve the high performance of algorithm implementation one should choose the best possible locality option. Studying the parallel algorithm locality is to estimate the number and volume of data communications. In this work, we formulate and prove the statements for computers with distributed memory that allow us to estimate the asymptotic volume of data communication operations. These estimation results are useful while comparing alternative versions of parallel algorithms during data communication cost analysis.

scholarly journals Asymptotic volume on Hilbert geometries

2013 ◽  
Vol 62 (5) ◽  
pp. 1431-1441 ◽  
Author(s):  
Constantin Vernicos
Keyword(s):  
Asymptotic Volume

scholarly journals Exact asymptotic volume and volume ratio of Schatten unit balls

2020 ◽  
Vol 257 ◽  
pp. 105457
Author(s):  
Zakhar Kabluchko ◽  
Joscha Prochno ◽  
Christoph Thäle
Keyword(s):  
Volume Ratio ◽  
Asymptotic Volume

scholarly journals A necessary and sufficient condition for some steady Ricci solitons to have positive asymptotic volume ratio

2013 ◽  
Vol 21 (2) ◽  
pp. 131-139
Author(s):  
Xiang Gao
Keyword(s):  
Volume Ratio ◽  
Ricci Soliton ◽  
Ricci Solitons ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Gradient Ricci Solitons ◽  
Necessary And Sufficient ◽  
Asymptotic Volume

Abstract In this paper, we firstly establish a useful ODE relationship between R1(c) and V1(c) on the steady Ricci soliton. Based on this, we obtain a necessary and sufficient condition for some complete noncompact steady gradient Ricci solitons to have positive asymptotic volume ratio.

scholarly journals Mean Curvature and Asymptotic Volume of Small Balls

2003 ◽  
Vol 110 (10) ◽  
pp. 947-950 ◽  
Author(s):  
Dominique Hulin ◽  
Marc Troyanov
Keyword(s):  
Mean Curvature ◽  
Asymptotic Volume

Asymptotic volume of Tori and geometry of convex bodies

1988 ◽  
Vol 44 (2) ◽  
pp. 579-586 ◽  
Author(s):  
I. K. Babenko
Keyword(s):  
Convex Bodies ◽  
Asymptotic Volume

scholarly journals On the asymptotic behavior of the dimension of spaces of harmonic functions with polynomial growth

2020 ◽  
Vol 2020 (762) ◽  
pp. 281-306 ◽  
Author(s):  
Xian-Tao Huang
Keyword(s):  
Asymptotic Behavior ◽  
Harmonic Functions ◽  
Tangent Cone ◽  
Polynomial Growth ◽  
Volume Growth ◽  
Volume Ratio ◽  
Growth Order ◽  
Maximal Volume ◽  
Nonnegative Ricci Curvature ◽  
Asymptotic Volume

AbstractSuppose {(M^{n},g)} is a Riemannian manifold with nonnegative Ricci curvature, and let {h_{d}(M)} be the dimension of the space of harmonic functions with polynomial growth of growth order at most d. Colding and Minicozzi proved that {h_{d}(M)} is finite. Later on, there are many researches which give better estimates of {h_{d}(M)}. In this paper, we study the behavior of {h_{d}(M)} when d is large. More precisely, suppose {(M^{n},g)} has maximal volume growth and has a unique tangent cone at infinity. Then when d is sufficiently large, we obtain some estimates of {h_{d}(M)} in terms of the growth order d, the dimension n and the asymptotic volume ratio {\alpha=\lim_{R\rightarrow\infty}\frac{\mathrm{Vol}(B_{p}(R))}{R^{n}}}. When {\alpha=\omega_{n}}, i.e., {(M^{n},g)} is isometric to the Euclidean space, the asymptotic behavior obtained in this paper recovers a well-known asymptotic property of {h_{d}(\mathbb{R}^{n})}.

scholarly journals Mean Curvature and Asymptotic Volume of Small Balls

2003 ◽  
Vol 110 (10) ◽  
pp. 947 ◽  
Author(s):  
Dominique Hulin ◽  
Marc Troyanov
Keyword(s):  
Mean Curvature ◽  
Asymptotic Volume
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