On the Noether gap theorem

A Gap Theorem for Differentially Algebraic Power Series

Number Theory ◽

10.1007/978-1-4757-4158-2_10 ◽

1991 ◽

pp. 211-214

Author(s):

Leonard Lipshitz ◽

Lee A. Rubel

Keyword(s):

Power Series ◽

Gap Theorem ◽

Algebraic Power Series

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On the Fabry-Ehrenpreis-Kawai gap theorem

Publications of the Research Institute for Mathematical Sciences ◽

10.2977/prims/1195176450 ◽

1987 ◽

Vol 23 (3) ◽

pp. 565-574 ◽

Cited By ~ 6

Author(s):

Carlos A. Berenstein ◽

Daniele C. Struppa

Keyword(s):

Gap Theorem

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A mini-gap theorem for Fourier series

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100042560 ◽

1968 ◽

Vol 64 (1) ◽

pp. 61-66 ◽

Cited By ~ 2

Author(s):

W. K. Hayman

Keyword(s):

Fourier Series ◽

Gap Theorem ◽

Image Position

Suppose thatbelongs to L2( − π, π). If most of the coefficients vanish then f (x) cannot be too small in a certain interval without being small generally. More precisely Ingham ((2), Theorem 1) has proved the followingTHEOREM A. Suppose that f (x) is given by (1·1) and that an = 0, except for a sequence n = nν, where nν+1 − nν ≥ C. Then given ∈ > 0 there exists a constant A (∈), such that we have for any real x1

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Optimal Curvature Estimates for Homogeneous Ricci Flows

International Mathematics Research Notices ◽

10.1093/imrn/rnx256 ◽

2017 ◽

Vol 2019 (14) ◽

pp. 4431-4468 ◽

Cited By ~ 3

Author(s):

Christoph Böhm ◽

Ramiro Lafuente ◽

Miles Simon

Keyword(s):

Homogeneous Space ◽

Homogeneous Spaces ◽

Convergence Result ◽

Einstein Metric ◽

Type I ◽

Extinction Time ◽

Ricci Flows ◽

Gap Theorem ◽

Ancient Solutions ◽

Curvature Estimates

AbstractWe prove uniform curvature estimates for homogeneous Ricci flows: For a solution defined on $[0,t]$ the norm of the curvature tensor at time $t$ is bounded by the maximum of $C(n)/t$ and $C(n)({\mathrm{scal}}(g(t)) - {\mathrm{scal}}(g(0)) )$. This is used to show that solutions with finite extinction time are Type I, immortal solutions are Type III and ancient solutions are Type I, with constants depending only on the dimension $n$. A further consequence is that a non-collapsed homogeneous ancient solution on a compact homogeneous space emerges from a unique Einstein metric on that space. The above curvature estimates follow from a gap theorem for Ricci-flatness on homogeneous spaces. This theorem is proved by contradiction, using a local $W^{2,p}$ convergence result which holds without symmetry assumptions.

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A gap theorem for Ricci-flat 4-manifolds

Differential Geometry and its Applications ◽

10.1016/j.difgeo.2015.02.012 ◽

2015 ◽

Vol 40 ◽

pp. 269-277

Author(s):

Atreyee Bhattacharya ◽

Harish Seshadri

Keyword(s):

Ricci Flat ◽

Gap Theorem

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Gap theorem on Kähler manifolds with nonnegative orthogonal bisectional curvature

Journal für die reine und angewandte Mathematik (Crelles Journal) ◽

10.1515/crelle-2019-0002 ◽

2020 ◽

Vol 2020 (763) ◽

pp. 111-127 ◽

Cited By ~ 2

Author(s):

Lei Ni ◽

Yanyan Niu

Keyword(s):

Liouville Theorem ◽

Holomorphic Functions ◽

Nonnegative Curvature ◽

Kähler Manifolds ◽

Kahler Manifolds ◽

Nonnegative Ricci Curvature ◽

Bisectional Curvature ◽

Plurisubharmonic Functions ◽

Dimension Estimate ◽

Gap Theorem

AbstractIn this paper we prove a gap theorem for Kähler manifolds with nonnegative orthogonal bisectional curvature and nonnegative Ricci curvature, which generalizes an earlier result of the first author [L. Ni, An optimal gap theorem, Invent. Math. 189 2012, 3, 737–761]. We also prove a Liouville theorem for plurisubharmonic functions on such a manifold, which generalizes a previous result of L.-F. Tam and the first author [L. Ni and L.-F. Tam, Plurisubharmonic functions and the structure of complete Kähler manifolds with nonnegative curvature, J. Differential Geom. 64 2003, 3, 457–524] and complements a recent result of Liu [G. Liu, Three-circle theorem and dimension estimate for holomorphic functions on Kähler manifolds, Duke Math. J. 165 2016, 15, 2899–2919].

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