Richard Hind webpage
Address: Department of Mathematics, University of Notre Dame, Notre Dame, IN
Mathematics in Architecture, Math 10270, Spring 2019.
Publications and Preprints
Filling by holomorphic disks with weakly pseudoconvex boundary conditions, Geom. Funct. Anal., 7(1997), 462-495.
Holomorphic filling of RP^3, Commun. Comtemp. Math., 3(2000), 349-363.
Symplectic geometry and the uniqueness of Grauert tubes, (with D. Burns), Geom. Funct. Anal., 11(2001), 1-10.
Antiholomorphic involutions on Stein manifolds, Intern. J. of Math., 14(2003), 479-487.
The geometry of Grauert tubes and complexifications of symmetric spaces, (with D. Burns and S. Halverscheid), Duke Math. J., 118(2003), 465-491.
Stein fillings of Lens spaces, Commun. Comtemp. Math., 5(2003), 967-982.
Lagrangian spheres in S^2 x S^2, Geom. Funct. Anal., 14(2004), 303-318.
Symplectic rigidity for Anosov hypersurfaces,(with D. Burns), J. Ergodic Theory and Dynamical Systems, 26(2006), 1399-1416.
Symplectic hypersurfaces in CP^3, Proc. of the Amer. Math. Soc., 134(2006), 1205-1211.
Lagrangian spheres in Stein surfaces, Asian J. Math., 16(2012), 1-36.
Isotopies of high genus Lagrangian surfaces, (with A. Ivrii), preprint.
Contact homology and Lens spaces (with M. Schwarz), preprint.
Symplectic capacities of domains in Euclidean space, International Math. Research Notices, 2006.
Cubulations of symplectic 4-manifolds, preprint.
Ruled 4-manifolds and isotopies of symplectic surfaces, (with A. Ivrii), Math Zeit., 265(2010), 639-652.
, (with J. von Bergmann), Ann. Global Anal. Geom., 37(2010), 413-427.
New obstructions to symplectic embeddings, (with E. Kerman), Invent. Math., 196(2014), 383-452. Correction: Invent. Math. 214(2018), 1023-1029.
Symplectic embedding of ellipsoids in dimension greater than four, (with O. Buse), Geom. and Top., 15(2011), 2091-2110.
Ellipsoid embeddings and symplectic packing stability, (with O. Buse), Compos. Math., 149(2013), 889-902.
On non-pure forms on almost-complex manifolds, (with C. Medori and A. Tomassini), Proc. of the Amer. Math. Soc., 142(2014), 3909-3922.
Embeddings of polydisks, (with S. Lisi), Selecta Math., 21(2015), 1099-1120. Erratum: Selecta Math., 23(2017), 813-815.
Symplectic folding and non-isotopic polydisks, Alg. and Geom. Top, 13(2013), 2171-2192.
Symplectomorphism groups of non-compact manifolds, orbifold balls, and a space of Lagrangians, (with M. Pinsonnault and W. Wu), J. Symp. Geom., 14(2016), 203-226.
Symplectic isotopies in dimension greater than four, J. Symp. Geom., 14(2016), 1033-1057.
On taming and compatible symplectic forms, (with C. Medori and A. Tomassini), J. Geom. Anal., 25(2015), 2360-2374.
Packing stability for symplectic 4-manifolds, (with O. Buse and E. Opshtein), Trans. of the Amer. Math. Soc., 368(2016), 8209-8222.
Some optimal embeddings of symplectic ellipsoids, J. Topology., 8(2015), 871-883.
Symplectic embeddings of products, (with D. Cristofaro-Gardiner), Comment. Math. Helv., 93(2018), 1-32.
Stabilized symplectic embeddings, in the book Complex and Symplectic Geometry, Springer INdAM Series 21(2017), 85-93.
The ghost stairs stabilize to sharp symplectic embedding obstructions, (with D. Cristofaro-Gardiner and D. McDuff), J. Topology, 11(2018), 309-378.
J-holomorphic cylinders between ellipsoids in dimension four, (with E. Kerman), J. Symp. Geom., 18(2020), 1221-1245.
On L^2 cohomology of almost Hermitian manifolds, (with A. Tomassini), J. Symp. Geom., 17(2019), 1773-1792.
Squeezing Lagrangian tori in dimension 4, (with E. Opshtein), Comment. Math. Helv., 95(2020), 535-567.
On the Anti-Invariant Cohomology of Almost Complex Manifolds, (with A. Tomassini), J. Geom. Anal., 31(2021), 4906-4922.
The shape invariant of symplectic ellipsoids, (with J. Zhang), preprint.
Higher symplectic capacities and the stabilized embedding problem for integral ellipsoids, (with D. Cristofaro-Gardiner and K. Siegel), J. Fixed Point Theory Appl. 24(2022), no. 2: Viterbo Volume, paper no. 49.
Hamiltonian knottedness and lifting paths from the shape invariant, (with J. Zhang), to appear in Compos. Math.
Packing Lagrangian tori, (with E. Kerman), to appear in Geom. and Top.
Families of almost complex structures and transverse (p,p) forms, (with C. Medori and A. Tomassini), J. Geom. Anal., 33(2013).
On the existence of symplectic barriers, (with P. Haim-Kislev and Y. Ostrover), preprint.
Almost complex blow-ups and positive closed (1,1)-forms on 4-dimensional almost complex manifolds, (with T. Sferruzza and A. Tomassini), preprint.
Boundaries of open symplectic manifolds and the failure of packing stability, (with D. Cristofaro-Gardiner), preprint.
On the agreement of symplectic capacities in high dimension, (with D. Cristofaro-Gardiner), preprint.
On the large-scale geometry of domains in an exact symplectic 4-manifold, (with D. Cristofaro-Gardiner), preprint.