A Few Snapshots from the Work of Mikhail Gromov

This collection is the result of a collaborative work of a number of mathematicians: M. Bestvina, D. Burago, Y. Eliashberg, F. Forstneric, L. Guth, A. Nabutovsky, A. Phillips, J. Roe and A. Vershik, coordinated and edited by D. Burago and Y. Eliashberg. Each contribution is however a single-authored paper. The papers are not unified by a common style or approach, they are indeed just snap-shots reflecting individual perception of their authors.

[1]  M. Hutchings.  Embedded contact homology and its applications , 2010, 1003.3209.

[2]  D. Burago,et al.  Minimality of planes in normed spaces , 2012, 1204.1543.

[3]  C. Taubes.  ${\rm Gr}Łongrightarrow{\rm SW}$: from pseudo-holomorphic curves to Seiberg-Witten solutions , 1999 .

[4]  M. Gromov,et al.  Spin and Scalar Curvature in the Presence of a Fundamental Group. I , 1980 .

[5]  M. Gromov,et al.  CAT(κ)-Spaces: Construction and Concentration , 2004 .

[6]  The Seiberg–Witten equations and the Weinstein conjecture II: More closed integral curves of the Reeb vector field , 2007, math/0702366.

[7]  H. Hofer.  Lusternik-Schnirelman-theory for Lagrangian intersections , 1988 .

[8]  Claude Viterbo,et al.  Symplectic topology as the geometry of generating functions , 1992 .

[9]  D. Burago,et al.  Area minimizers and boundary rigidity of almost hyperbolic metrics , 2010, 1011.1570.

[10]  T. Ekholm,et al.  Exact Lagrangian immersions with a single double point , 2011, 1111.5932.

[11]  S. Frankel,et al.  The Morse landscape of a Riemannian disk , 1993 .

[12]  A. Nabutovsky,et al.  Contracting the boundary of a Riemannian 2-disc , 2012, 1205.5474.

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[15]  M. Katz.  The filling radius of two-point homogeneous spaces , 1983 .

[16]  A. Floer,et al.  Morse theory for Lagrangian intersections , 1988 .

[17]  M. Gromov.  Oka’s principle for holomorphic sections of elliptic bundles , 1989 .

[18]  Yu. F. Borisov.  Irregular C1,β-Surfaces with an Analytic Metric , 2004 .

[19]  On Asymptotic Isoperimetric Constant of Tori , 1998 .

[20]  M. Hutchings.  Recent progress on symplectic embedding problems in four dimensions , 2011, Proceedings of the National Academy of Sciences.

[21]  Geometry of differential equations , 2008 .

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[23]  C. Taubes.  The Seiberg–Witten equations and the Weinstein conjecture , 2006, math/0702366.

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[26]  M. Gromov,et al.  Singularities, Expanders and Topology of Maps. Part 1: Homology Versus Volume in the Spaces of Cycles , 2009 .

[27]  A. Nabutovsky,et al.  The length of the shortest closed geodesic on a 2-dimensional sphere , 2002 .

[28]  Jirí Matousek,et al.  Polynomial-Time Homology for Simplicial Eilenberg–MacLane Spaces , 2012, Found. Comput. Math..

[29]  Metaphors in Systolic Geometry , 2010, 1003.4247.

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[34]  F. Forstnerič.  The Oka principle for sections of stratified fiber bundles , 2007, 0705.0591.

[35]  Jean-Camille Birget,et al.  Isoperimetric and isodiametric functions of groups , 1998 .

[36]  S. Ivanov,et al.  On asymptotic volume of Finsler tori, minimal surfaces in normed spaces, and symplectic filling volume , 2002 .

[37]  S. Sabourau,et al.  DIASTOLIC AND ISOPERIMETRIC INEQUALITIES ON SURFACES , 2024, 2402.01554.

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[44]  D. Burago,et al.  A Course in Metric Geometry , 2001 .

[45]  Camillo De Lellis,et al.  The $h$-principle and the equations of fluid dynamics , 2011, 1111.2700.

[46]  F. Forstnerič,et al.  Oka's principle for holomorphic fiber bundles with sprays , 2000, math/0305238.

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[50]  A. Nabutovsky,et al.  Upper bounds on the length of a shortest closed geodesic and quantitative Hurewicz theorem , 2003 .

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[58]  S. Ivanov,et al.  Hyperbolic groups and their quotients of bounded exponents , 1996 .

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[70]  A. Floer,et al.  The unregularized gradient flow of the symplectic action , 1988 .

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[72]  M. Gromov,et al.  Nonsingular mappings of Stein manifolds , 1971 .

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[74]  D. Burago,et al.  Boundary rigidity and filling volume minimality of metrics close to a flat one , 2010 .

[75]  F. Forstnerič,et al.  Survey of Oka theory , 2010, 1009.1934.

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[81]  L. Guth.  Volumes of balls in large Riemannian manifolds , 2006, math/0610212.

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[83]  S. Sabourau.  Filling Radius and Short Closed Geodesics of the $2$-Sphere , 2004 .

[84]  Global and Local Volume Bounds and the Shortest Geodesic Loops , 2004 .

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[88]  M. Gromov,et al.  Positive Curvature, Macroscopic Dimension, Spectral Gaps and Higher Signatures , 1996 .

[89]  Zoltan Szabo,et al.  Holomorphic disks and three-manifold invariants: Properties and applications , 2001 .

[90]  C. Croke,et al.  A Zoll Counterexample to a Geodesic Length Conjecture , 2007, 0711.1229.

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[92]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[93]  M. Gromov,et al.  The Classification of Simply Connected Manifolds of Positive Scalar Curvature Author ( s ) : , 2010 .

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[95]  L. Polterovich,et al.  Symplectic packings and algebraic geometry , 1994 .

[96]  A. Vershik.  Dynamics of metrics in measure spaces and their asymptotic invariants , 2009 .

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[103]  M. Gromov.  Filling Riemannian manifolds , 1983 .

[104]  Ian Agol,et al.  The virtual Haken conjecture , 2012, 1204.2810.

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[106]  L. Guth.  Symplectic embeddings of polydisks , 2007, 0709.1957.

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[109]  Yann Ollivier,et al.  A January 2005 invitation to random groups , 2005, Ensaios Matemáticos.

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[120]  Quantitative algebraic topology and Lipschitz homotopy , 2013, Proceedings of the National Academy of Sciences.

[121]  M. Gromov.  Singularities, Expanders and Topology of Maps. Part 2: from Combinatorics to Topology Via Algebraic Isoperimetry , 2010 .

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