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Autor:
Wen Shuai Jiang
Publikováno v:
Acta Mathematica Sinica, English Series. 37:1751-1767
In this paper, we consider Ricci flow on four dimensional closed manifold with bounded scalar curvature, noncollasping volume and bounded diameter. Under such conditions, we can show that the manifold has finitely many diffeomorphism types, which gen
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6b28621bccf419d66025ccf32e83b35a
https://doi.org/10.1007/s10114-021-0149-4
https://doi.org/10.1007/s10114-021-0149-4
Autor:
Frédéric Robert, Jérôme Vétois
Publikováno v:
International Mathematics Research Notices. 2023:901-931
Given a closed manifold $(M^n,g)$, $n\geq 3$, Druet [5, 7] proved that a necessary condition for the existence of energy-bounded blowing-up solutions to perturbations of the equation $$ \begin{align*} &\Delta_gu+h_0u=u^{\frac{n+2}{n-2}},\ u>0 \ \text
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::6b7b8748f5fde6ec6181eea3852e854c
https://doi.org/10.1093/imrn/rnab286
https://doi.org/10.1093/imrn/rnab286
Autor:
Alberto Abbondandolo, Pietro Majer
Publikováno v:
Journal of Topology and Analysis. :1-57
We prove that a Morse-Smale gradient-like flow on a closed manifold has a "system of compatible invariant stable foliations" that is analogous to the object introduced by Palis and Smale in their proof of the structural stability of Morse-Smale diffe
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::9be7a472a4b78f315377521f73b8184c
https://doi.org/10.1142/s1793525321500527
https://doi.org/10.1142/s1793525321500527
Autor:
Xin Zhou, Antoine Song
Publikováno v:
Geometric and Functional Analysis. 31:948-980
Let $$M^{n+1}$$ be a closed manifold of dimension $$3\le n+1\le 7$$ . We show that for a $$C^\infty $$ -generic metric g on M, to any connected, closed, embedded, 2-sided, stable, minimal hypersurface $$S\subset (M,g)$$ corresponds a sequence of clos
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::dfb6bffd65fa5b1960082aa5cece2b9a
https://doi.org/10.1007/s00039-021-00571-7
https://doi.org/10.1007/s00039-021-00571-7
Autor:
Alexandre Rocha
Publikováno v:
Regular and Chaotic Dynamics. 26:293-304
Let $$M$$ be a closed manifold and $$L$$ an exact magnetic Lagrangian. In this paper we prove that there exists a residual set $$\mathcal{G}$$ of $$H^{1}\left(M;\mathbb{R}\right)$$ such that the property $${\widetilde{\mathcal{M}}}\left(c\right)={\wi
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::94d027be1a9a9290759719c4fcd78b62
https://doi.org/10.1134/s1560354721030060
https://doi.org/10.1134/s1560354721030060
Autor:
Tianyu Wang, Daniel J. Thompson
Publikováno v:
Communications in Mathematical Physics. 385:1213-1243
We consider the geodesic flow for a rank one non-positive curvature closed manifold. We prove an asymptotic version of the Central Limit Theorem for families of measures constructed from regular closed geodesics converging to the Bowen-Margulis-Kniep
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::72efd98144c6ac4cb084d0f4112ebf24
https://doi.org/10.1007/s00220-021-04062-6
https://doi.org/10.1007/s00220-021-04062-6
Autor:
Shu Shen, Jianqing Yu
Publikováno v:
Journal de l’École polytechnique — Mathématiques. 8:585-607
We introduce a Milnor metric on the determinant line of the cohomology of the underlying closed manifold with coefficients in a flat vector bundle, by means of interactions between the fixed points and the closed orbits of a Morse-Smale flow. This al
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4d0fbd8fc9f82d365ec44ea05434c6b6
https://doi.org/10.5802/jep.154
https://doi.org/10.5802/jep.154
Publikováno v:
Mathematische Annalen. 379:1605-1622
Answering a question of Uspenskij, we prove that if X is a closed manifold of dimension 2 or higher or the Hilbert cube, then the universal minimal flow of $${\text {Homeo}}(X)$$ is not metrizable. In dimension 3 or higher, we also show that the mini
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::268aec38cfbee5358407b9391dff97b9
https://doi.org/10.1007/s00208-021-02146-1
https://doi.org/10.1007/s00208-021-02146-1
Autor:
Christoforos Neofytidis
Publikováno v:
Geometriae Dedicata. 213:325-337
A long-standing conjecture asserts that any Anosov diffeomorphism of a closed manifold is finitely covered by a diffeomorphism which is topologically conjugate to a hyperbolic automorphism of a nilpotent manifold. In this paper, we show that any clos
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b080643ce8cbed9269d385952047c4e2
https://doi.org/10.1007/s10711-020-00583-x
https://doi.org/10.1007/s10711-020-00583-x