scholarly journals On the Maximal Rate of Convergence Under the Ricci Flow

2020 ◽  
Author(s):  
Brett Kotschwar
Keyword(s):  
Rate Of Convergence ◽  
Ricci Flow ◽  
Closed Manifold ◽  
Maximal Rate ◽  
Exponential Rate ◽  
Normalized Ricci Flow ◽  
Self Similar

Abstract We estimate from above the rate at which a solution to the normalized Ricci flow on a closed manifold may converge to a limit soliton. Our main result implies that any solution that converges modulo diffeomorphisms to a soliton faster than any fixed exponential rate must itself be self-similar.

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (04) ◽  
pp. 733-740
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn (x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G ∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

EIGENVALUES OF GEOMETRIC OPERATORS RELATED TO THE WITTEN LAPLACIAN UNDER THE RICCI FLOW

2017 ◽  
Vol 59 (3) ◽  
pp. 743-751
Author(s):  
SHOUWEN FANG ◽  
FEI YANG ◽  
PENG ZHU
Keyword(s):  
Riemannian Manifold ◽  
Scalar Curvature ◽  
Ricci Flow ◽  
Compact Riemannian Manifold ◽  
Laplacian Operator ◽  
Witten Laplacian ◽  
Normalized Ricci Flow ◽  
Geometric Operator

AbstractLet (M, g(t)) be a compact Riemannian manifold and the metric g(t) evolve by the Ricci flow. In the paper, we prove that the eigenvalues of geometric operator −Δφ + $\frac{R}{2}$ are non-decreasing under the Ricci flow for manifold M with some curvature conditions, where Δφ is the Witten Laplacian operator, φ ∈ C2(M), and R is the scalar curvature with respect to the metric g(t). We also derive the evolution of eigenvalues under the normalized Ricci flow. As a consequence, we show that compact steady Ricci breather with these curvature conditions must be trivial.

The exponential rate of convergence of the distribution of the maximum of a random walk. Part II

1976 ◽  
Vol 13 (4) ◽  
pp. 733-740 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Random Walk ◽  
Rate Of Convergence ◽  
Real Line ◽  
Exponential Convergence ◽  
Exponential Rate ◽  
The Real ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence ◽  
Successive Maximum

Let Gn (x) be the distribution of the nth successive maximum of a random walk on the real line. Under conditions typical for complete exponential convergence, the decay of Gn (x) – limn→∞ Gn(x) is asymptotically equal to H(x) γn n–3/2 as n → ∞where γ < 1 and H(x) a function solely depending on x. For the case of drift to + ∞, G∞(x) = 0 and the result is new; for drift to – ∞we give a new proof, simplifying and correcting an earlier version in [9].

The exponential rate of convergence of the distribution of the maximum of a random walk

1975 ◽  
Vol 12 (02) ◽  
pp. 279-288 ◽  
Author(s):  
N. Veraverbeke ◽  
J. L. Teugels
Keyword(s):  
Distribution Function ◽  
Random Walk ◽  
Rate Of Convergence ◽  
Exponential Convergence ◽  
Random Variables ◽  
Limiting Distribution ◽  
Partial Sums ◽  
Exponential Rate ◽  
Distribution Of The Maximum ◽  
Exponential Rate Of Convergence

Let Gn (x) be the distribution function of the maximum of the successive partial sums of independent and identically distributed random variables and G(x) its limiting distribution function. Under conditions, typical for complete exponential convergence, the decay of Gn (x) — G(x) is asymptotically equal to c.H(x)n −3/2 γn as n → ∞ where c and γ are known constants and H(x) is a function solely depending on x.

scholarly journals An Adaptive Observer with Exponential Rate of Convergence

1982 ◽  
Vol 18 (4) ◽  
pp. 343-348 ◽  
Author(s):  
Zenta IWAI ◽  
Makoto SATO ◽  
Akira INOUE ◽  
Kazuo MANO
Keyword(s):  
Rate Of Convergence ◽  
Adaptive Observer ◽  
Exponential Rate ◽  
Exponential Rate Of Convergence

The normalized Ricci flow and homology in Lagrangian submanifolds of generalized complex space forms

2020 ◽  
Vol 17 (06) ◽  
pp. 2050094 ◽  
Author(s):  
Fatemah Mofarreh ◽  
Akram Ali ◽  
Wan Ainun Mior Othman
Keyword(s):  
Fundamental Form ◽  
Ricci Flow ◽  
Complex Space ◽  
Space Form ◽  
Second Fundamental Form ◽  
Complex Space Form ◽  
Standard Sphere ◽  
The Second Fundamental Form ◽  
Generalized Complex ◽  
Normalized Ricci Flow

In this paper, we prove that a simply connected Lagrangian submanifold in the generalized complex space form is diffeomorphic to standard sphere [Formula: see text] and the normalized Ricci flow converges to a constant curvature metric, provided its squared norm of the second fundamental form satisfies some upper bound depending only on the squared norm of the mean curvature vector field, the constant sectional curvature, and the dimension of the Lagrangian immersion of the ambient space. Next, we conclude that stable currents do not exist and homology groups vanish in a compact real submanifold of the general complex space form, provided that the second fundamental form satisfies some extrinsic conditions. We show that our results improve some previous results.

scholarly journals The Long-Time Behavior of the Ricci Tensor under the Ricci Flow

Geometry ◽  
2013 ◽  
Vol 2013 ◽  
pp. 1-4 ◽  
Author(s):  
Christian Hilaire
Keyword(s):  
Ricci Flow ◽  
Ricci Tensor ◽  
Closed Manifold ◽  
Time Behavior ◽  
Dimensional Manifold ◽  
Long Time Behavior ◽  
Bounded Curvature ◽  
3 Dimensional ◽  
Long Time ◽  
Uniformly Bounded

We show that, given an immortal solution to the Ricci flow on a closed manifold with uniformly bounded curvature and diameter, the Ricci tensor goes to zero as . We also show that if there exists an immortal solution on a closed 3-dimensional manifold such that the product of the curvature and the square of the diameter is uniformly bounded, then this solution must be of type III.

scholarly journals Exponential rate of convergence in current reservoirs

Bernoulli ◽  
2015 ◽  
Vol 21 (3) ◽  
pp. 1844-1854 ◽  
Author(s):  
Anna De Masi ◽  
Errico Presutti ◽  
Dimitrios Tsagkarogiannis ◽  
Maria Eulalia Vares
Keyword(s):  
Rate Of Convergence ◽  
Exponential Rate ◽  
Exponential Rate Of Convergence
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