Free to readers and authors, Electronic Research Announcements in Mathematical Sciences rapidly publishes announcements of significant advances in all branches of mathematics and short complete papers of original research (up to about 15 journal pages). Research announcements are an opportunity for lucid exposition of ideas and context unburdened by technical detail. All articles should be designed to communicate their contents to a broad mathematical audience and must meet high standards for mathematical content and clarity. After review and acceptance by the entire Editorial Board, articles enter production for immediate publication.

ERA is a continuation of Electronic Research Announcements of the AMS published by the American Mathematical Society from 1995 to the middle of 2007. After over two decades of leading this journal, Svetlana Katok became Founding Editor Emerita in January 2017.

  • AIMS is a member of COPE. All AIMS journals adhere to the publication ethics and malpractice policies outlined by COPE.
  • Publishes 1 volume a year.
  • Publishes online only.
  • Archived in Portico and CLOCKSS.
  • ERA-MS is a publication of the American Institute of Mathematical Sciences. All rights reserved.

Note: “Most Cited” is by Cross-Ref , and “Most Downloaded” is based on available data in the new website.

Zermelo deformation of finsler metrics by killing vector fields
Patrick Foulon and Vladimir S. Matveev
2018, 25: 1-7 doi: 10.3934/era.2018.25.001 +[Abstract](615) +[HTML](373) +[PDF](299.36KB)
Abstract:

We show how geodesics, Jacobi vector fields, and flag curvature of a Finsler metric behave under Zermelo deformation with respect to a Killing vector field. We also show that Zermelo deformation with respect to a Killing vector field of a locally symmetric Finsler metric is also locally symmetric.

Hyperbolic dynamics of discrete dynamical systems on pseudo-riemannian manifolds
Mohammadreza Molaei
2018, 25: 8-15 doi: 10.3934/era.2018.25.002 +[Abstract](516) +[HTML](314) +[PDF](398.47KB)
Abstract:

We consider a discrete dynamical system on a pseudo-Riemannian manifold and we determine the concept of a hyperbolic set for it. We insert a condition in the definition of a hyperbolic set which implies to the unique decomposition of a part of tangent space (at each point of this set) to two unstable and stable subspaces with exponentially increasing and exponentially decreasing dynamics on them. We prove the continuity of this decomposition via the metric created by a torsion-free pseudo-Riemannian connection. We present a global attractor for a diffeomorphism on an open submanifold of the hyperbolic space \begin{document}$H^2(1)$\end{document} which is not a hyperbolic set for it.

Signatures, sums of hermitian squares and positive cones on algebras with involution
Vincent Astier and Thomas Unger
2018, 25: 16-26 doi: 10.3934/era.2018.25.003 +[Abstract](542) +[HTML](313) +[PDF](379.4KB)
Abstract:

We provide a coherent picture of our efforts thus far in extending real algebra and its links to the theory of quadratic forms over ordered fields in the noncommutative direction, using hermitian forms and "ordered" algebras with involution.

On the torsion in the center conjecture
Vitali Kapovitch, Anton Petrunin and Wilderich Tuschmann
2018, 25: 27-35 doi: 10.3934/era.2018.25.004 +[Abstract](443) +[HTML](297) +[PDF](336.41KB)
Abstract:

We present a condition for towers of fiber bundles which implies that the fundamental group of the total space has a nilpotent subgroup of finite index whose torsion is contained in its center. Moreover, the index of the subgroup can be bounded in terms of the fibers of the tower.

Our result is motivated by the conjecture that every almost nonnegatively curved closed \begin{document}$ m $\end{document}-dimensional manifold \begin{document}$ M $\end{document} admits a finite cover \begin{document}$ \tilde M $\end{document} for which the number of leafs is bounded in terms of \begin{document}$ m $\end{document} such that the torsion of the fundamental group \begin{document}$ π_1 \tilde M $\end{document} lies in its center.

On the norm continuity of the hk-fourier transform
Juan H. Arredondo, Francisco J. Mendoza and Alfredo Reyes
2018, 25: 36-47 doi: 10.3934/era.2018.25.005 +[Abstract](411) +[HTML](263) +[PDF](364.71KB)
Abstract:

In this work we study the Cosine Transform operator and the Sine Transform operator in the setting of Henstock-Kurzweil integration theory. We show that these related transformation operators have a very different behavior in the context of Henstock-Kurzweil functions. In fact, while one of them is a bounded operator, the other one is not. This is a generalization of a result of E. Liflyand in the setting of Lebesgue integration.

Explicit geodesics in Gromov-Hausdorff space
Samir Chowdhury and Facundo Mémoli
2018, 25: 48-59 doi: 10.3934/era.2018.25.006 +[Abstract](310) +[HTML](197) +[PDF](397.37KB)
Abstract:

We provide an alternative, constructive proof that the collection \begin{document}${\mathcal{M}}$\end{document} of isometry classes of compact metric spaces endowed with the Gromov-Hausdorff distance is a geodesic space. The core of our proof is a construction of explicit geodesics on \begin{document}${\mathcal{M}}$\end{document}. We also provide several interesting examples of geodesics on \begin{document}${\mathcal{M}}$\end{document}, including a geodesic between \begin{document}${\mathbb{S}}^0$\end{document} and \begin{document}${\mathbb{S}}^n$\end{document} for any \begin{document}$n\geq 1$\end{document}.

Notes on monotone Lagrangian twist tori
Yuri Chekanov and Felix Schlenk
2010, 17: 104-121 doi: 10.3934/era.2010.17.104 +[Abstract](737) +[PDF](260.8KB) Cited By(8)
Research announcement: The structure of groups with a quasiconvex hierarchy
Daniel T. Wise
2009, 16: 44-55 doi: 10.3934/era.2009.16.44 +[Abstract](2954) +[PDF](2176.9KB) Cited By(7)
The spectrum of the weakly coupled Fibonacci Hamiltonian
David Damanik and Anton Gorodetski
2009, 16: 23-29 doi: 10.3934/era.2009.16.23 +[Abstract](894) +[PDF](143.8KB) Cited By(6)
Upper bounds for Steklov eigenvalues on surfaces
Alexandre Girouard and Iosif Polterovich
2012, 19: 77-85 doi: 10.3934/era.2012.19.77 +[Abstract](734) +[PDF](126.0KB) Cited By(6)
Infinite determinantal measures
Alexander I. Bufetov
2013, 20: 12-30 doi: 10.3934/era.2013.20.12 +[Abstract](732) +[PDF](474.9KB) Cited By(6)
Higher pentagram maps, weighted directed networks, and cluster dynamics
Michael Gekhtman, Michael Shapiro, Serge Tabachnikov and Alek Vainshtein
2012, 19: 1-17 doi: 10.3934/era.2012.19.1 +[Abstract](659) +[PDF](262.3KB) Cited By(3)
Hölder cocycles and ergodic integrals for translation flows on flat surfaces
Alexander I. Bufetov
2010, 17: 34-42 doi: 10.3934/era.2010.17.34 +[Abstract](912) +[PDF](173.1KB) Cited By(3)
Sharp weighted estimates for approximating dyadic operators
David Cruz-Uribe, SFO, José María Martell and Carlos Pérez
2010, 17: 12-19 doi: 10.3934/era.2010.17.12 +[Abstract](800) +[PDF](160.5KB) Cited By(3)
An inverse theorem for the Gowers $U^{s+1}[N]$-norm
Ben Green, Terence Tao and Tamar Ziegler
2011, 18: 69-90 doi: 10.3934/era.2011.18.69 +[Abstract](1046) +[PDF](308.3KB) Cited By(2)
$\alpha$-concave functions and a functional extension of mixed volumes
Vitali Milman and Liran Rotem
2013, 20: 1-11 doi: 10.3934/era.2013.20.1 +[Abstract](718) +[PDF](356.7KB) Cited By(2)
Zermelo deformation of finsler metrics by killing vector fields
Patrick Foulon and Vladimir S. Matveev
2018, 25: 1-7 doi: 10.3934/era.2018.25.001 +[Abstract](615) +[HTML](373) +[PDF](299.36KB) PDF Downloads(88)
Signatures, sums of hermitian squares and positive cones on algebras with involution
Vincent Astier and Thomas Unger
2018, 25: 16-26 doi: 10.3934/era.2018.25.003 +[Abstract](542) +[HTML](313) +[PDF](379.4KB) PDF Downloads(62)
Desingularization of surface maps
Erica Clay, Boris Hasselblatt and Enrique Pujals
2017, 24: 1-9 doi: 10.3934/era.2017.24.001 +[Abstract](740) +[HTML](386) +[PDF](638.6KB) PDF Downloads(58)
On the norm continuity of the hk-fourier transform
Juan H. Arredondo, Francisco J. Mendoza and Alfredo Reyes
2018, 25: 36-47 doi: 10.3934/era.2018.25.005 +[Abstract](411) +[HTML](263) +[PDF](364.71KB) PDF Downloads(53)
Hyperbolic dynamics of discrete dynamical systems on pseudo-riemannian manifolds
Mohammadreza Molaei
2018, 25: 8-15 doi: 10.3934/era.2018.25.002 +[Abstract](516) +[HTML](314) +[PDF](398.47KB) PDF Downloads(53)
On the torsion in the center conjecture
Vitali Kapovitch, Anton Petrunin and Wilderich Tuschmann
2018, 25: 27-35 doi: 10.3934/era.2018.25.004 +[Abstract](443) +[HTML](297) +[PDF](336.41KB) PDF Downloads(51)
Explicit geodesics in Gromov-Hausdorff space
Samir Chowdhury and Facundo Mémoli
2018, 25: 48-59 doi: 10.3934/era.2018.25.006 +[Abstract](310) +[HTML](197) +[PDF](397.37KB) PDF Downloads(44)
Existence and uniqueness of weak solutions for a class of nonlinear parabolic equations
Peiying Chen
2017, 24: 38-52 doi: 10.3934/era.2017.24.005 +[Abstract](1044) +[HTML](484) +[PDF](382.7KB) PDF Downloads(42)
Sharpness of the Brascamp–Lieb inequality in Lorentz spaces
Neal Bez, Sanghyuk Lee, Shohei Nakamura and Yoshihiro Sawano
2017, 24: 53-63 doi: 10.3934/era.2017.24.006 +[Abstract](1244) +[HTML](611) +[PDF](407.1KB) PDF Downloads(40)
The orbifold Langer-Miyaoka-Yau Inequality and Hirzebruch-type inequalities
Piotr Pokora
2017, 24: 21-27 doi: 10.3934/era.2017.24.003 +[Abstract](778) +[HTML](404) +[PDF](281.0KB) PDF Downloads(37)

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