Preprints and Links to Papers


Bilinear generalized Radon transforms in the plane

by Allan Greenleaf, Alex Iosevich, Ben Krause and Allen Liu

Posted April 4, 2017; submitted.

This article is available as an ArXiv preprint .

Propagation and recovery of singularities in the inverse conductivity problem

by Allan Greenleaf, Matti Lassas, M. Santacesaria, S. Siltanen, Gunther Uhlmann

Posted Oct. 6, 2016; submitted.

This article is available as an ArXiv preprint .

Superdimensional Metamaterial Resonators

by Allan Greenleaf, Henrik Kettunen, Yaroslav Kurylev, Matti Lassas, Gunther Uhlmann

Posted Sept. 11, 2014; submitted.

This article is available as an ArXiv preprint .

On necklaces inside thin subsets of R^d

by Allan Greenleaf, Alex Iosevich, and Malabika Pramanik

Posted Sept. 9, 2014; submitted.

This article is available as an ArXiv preprint .

A group-theoretic viewpoint on Erdos-Falconer problems and the Mattila integral

by Allan Greenleaf, Alex Iosevich, Bochen Liu and Eyvindur Palsson

Posted June 15, 2013; revised August 26, 2013, and April 10, 2014. Revista Mathematica Ibereoamerica, to appear.

This article is available as an ArXiv preprint .

Restricted convolution inequalities, multilinear operators and applications

by Dan-Andrei Geba, Allan Greenleaf, Alex Iosevich, Eyvindur Palsson and Eric Sawyer

Posted September 28, 2012; Math. Res. Lett., 20 (2013), no.4, 675-694.

This article is available as an ArXiv preprint . See also Comments and errata .

Multilinear generalized Radon transforms and point configurations

by Loukas Grafakos, Allan Greenleaf, Alex Iosevich and Eyvindur Palsson

Posted April 19, 2012; Forum Mathematicum, published online Sept. 2013, DOI: 10.1515/forum-2013-0128.

This article is available as an ArXiv preprint .


On volumes determined by subsets of Euclidean space

by Allan Greenleaf, Alex Iosevich and Mihalis Mourgoglou

Posted October 31, 2011; Forum mathematicum , 27, no. 1, (2015),635 - 646. Published online , June 19, 2013 (subscription req.).

This article is available as an ArXiv preprint .


Cloaked electromagnetic, acoustic and quantum amplifiers via transformation optics

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas, Ulf Leonhardt and Gunther Uhlmann

Proc. National Acad. Sci., published online before print June 14, 2012, doi: 10.1073/pnas.1116864109; print: 26 June 2012, v. 109, no. 26, 10169-10174.

On triangles determined by subsets of the Euclidean plane, the associated bilinear operators and applications to discrete geometry

by Allan Greenleaf and Alex Iosevich

Posted September 14, 2010; revised Oct. 19, 2011. Analysis & PDE 5-2 (2012), 397-409. DOI 10.2140/apde.2012.5.397.

This article is available as an ArXiv preprint .

A multi-dimensional resolution of singularities with applications to analysis

by Tristan Collins, Allan Greenleaf and Malabika Pramanik

Posted July 4, 2010; American Journal of Mathematics, 135, no. 5, (2013), 1179-1252. Published online, DOI: 10.1353/ajm.2013.0042 (subscription req.).

This article is also available as an ArXiv preprint .

Fourier integral operators with open umbrellas and seismic inversion for cusp caustics

by Raluca Felea and Allan Greenleaf

Posted January 27, 2010; Mathematical Research Letters , 17 (2010), 867-886.

This article is available as an ArXiv preprint .


Cloaking a Sensor via Transformation Optics

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Posted December 9, 2009; revised Oct. 31, 2010. Phys. Rev. E 83, 016603 (2011) .

This article is available as an ArXiv preprint .


An FIO calculus for marine seismic imaging, II: Sobolev estimates

by Raluca Felea, Allan Greenleaf and Malabika Pramanik

Posted March 10, 2009. The final publication is available at www.springerlink.com: Mathematische Annalen, DOI: 10.1007/s00208-011-0644-5.

A preliminary version is available as an

ArXiv preprint .


Approximate quantum and acoustic cloaking

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Posted December 9, 2008; to appear, J. Spectral Theory

This article is available as an


Cloaking Devices, Electromagnetic Wormholes, and Transformation Optics

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

SIAM Review 51, no. 1, (2009), 3-33.

[survey article]


Invisibility and inverse problems

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Bull. Amer. Math. Soc. 46 (2009), 55-97.

[survey article]


Approximate quantum cloaking and almost trapped states

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Physical Review Letters 101, no. 22, 220404 (2008) (subscription required.)

Originally posted as an ArXiv preprint June 1, 2008; revised August 19, 2008.


Isotropic transformation optics: approximate acoustic and quantum cloaking

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

New Jour. Phys. 10 (2008) 115024

Originally posted as an ArXiv preprint May 31, 2008; revised August 1, 2008.


Comment on "Scattering Theory Derivation of a 3D Acoustic Cloaking Shell"

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Posted January 22, 2008.

This article is available as an


Improvement of cylindrical cloaking with the SHS lining

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Optics Express, Vol. 15, Issue 20, pp. 12717-12734 (2007)

Posted July 9, 2007; revised Sept. 14, 2007.


Electromagnetic wormholes via handlebody constructions

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Communications in Mathematical Physics, 281, no. 2 (2008), 369-385 (subscription required).

Posted April 6, 2007.


This article is available as an


Electromagnetic wormholes and virtual magnetic monopoles from metamaterials

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Physical Review Letters, 99, no. 18, 183901 (2007) (subscription required.)

Posted March 21, 2007; revised August 14, 2007.

This article is also available in preliminary form as a


Full-wave invisibility of active devices at all frequencies

by Allan Greenleaf, Yaroslav Kurylev, Matti Lassas and Gunther Uhlmann

Communications in Mathematical Physics, 275, no. 3 (2007), 749-789 (subscription required).

Posted November 7, 2006; revised January 11, 2007; March 16, 2007.

This article is also available in preliminary form as an


Average decay estimates for Fourier transforms of measures supported on curves

by Luca Brandolini, Giacomo Gigante, Allan Greenleaf,

Alexander Iosevich, Andreas Seeger and Giancarlo Travaglini

Posted July 4, 2006; revised, July 13, 2006; Journal of Geometric Analysis, 17 (2007), 15-40.

This article is available as an


An FIO calculus for marine seismic imaging:

folds and cross caps

by Raluca Felea and Allan Greenleaf

Posted May 31, 2006; revised Feb. 13, 2007; Comm. in P.D.E. , 33 (2008), 45-77 .

A preliminary version of this article is available as an


Oscillatory integral operators with homogeneous

polynomial phases in several variables

by Allan Greenleaf, Malabika Pramanik and Wan Tang

Posted May 3, 2006; revised October 26, 2006; Jour. of Functional Analysis , 244 (2007), 444-487.

This article is available as an


$L^p - L^{p'}$ estimates for overdetermined Radon transforms

by Luca Brandolini, Allan Greenleaf and Giancarlo Travaglini

Posted December 16, 2003; revised January 31, 2005.

Transactions of the A.M.S, 359 (2007), 2559-2575.

This article is available as a


On nonuniqueness for Calderon's inverse problem

by Allan Greenleaf, Matti Lassas and Gunther Uhlmann

Posted March 3, 2003; revised June 30, 2003.

Mathematical Research Letters, 10 (2003), 685-693.

This article is available as a


Anisotropic conductivities that cannot be detected by EIT

by Allan Greenleaf, Matti Lassas and Gunther Uhlmann

Posted January 3, 2003; revised January 27, 2003.

Physiological Measurement, special issue, Proceedings of Mummy Range Workshop on EIT, 24 (2003), 413-419.

This article is available as a


The Calderon problem for conormal potentials, I:

Global uniqueness and reconstruction

by Allan Greenleaf, Matti Lassas and Gunther Uhlmann

Posted December 12, 2001; final revision, October 4, 2002

Communications on Pure and Applied Mathematics, 56 (2003), no. 3, 328-352.

This article is available as a


Oscillatory and Fourier integral operators

with degenerate canonical relations

by Allan Greenleaf and Andreas Seeger

Posted July 13, 2001; final revision, February 21, 2002.

Appeared in the Proceedings of the El Escorial 2000 Conference

(mostly expository, but contains some new material)

This article is available as a


Oscillatory integral operators

with low-order degeneracies

by Allan Greenleaf and Andreas Seeger

Posted July 26, 2000; final revision posted February 20, 2002

Appeared in Duke Math. Jour., 112 (2002), 397-420.

This article is available as a


Local uniqueness for the Dirichlet-to-Neumann

map via the two-plane transform

by Allan Greenleaf and Gunther Uhlmann

Duke Math. Jour., 108 (2001), 599-617.

This article is available as a


Characteristic space-time estimates

for the wave equation

by Allan Greenleaf and Gunther Uhlmann

Posted September 1, 1999; revised November 15, 1999

Mathematische Zeitschrift, 236 (2001), 113-131.

This article is available in PostScript format.


Estimates for generalized Radon transforms in

three and four dimensions

by Allan Greenleaf, Andreas Seeger and Stephen Wainger

Posted January 20, 1999

survey article, appeared in Contemporary Mathematics, v. 251 , Proceedings of the Ehrenpreis Conference

This article is available in PostScript format.


On X-ray transforms for rigid line complexes

and integrals over curves in R^4

by Allan Greenleaf, Andreas Seeger and Stephen Wainger

Posted January 30, 1998

appeared in Proc. Amer. Math. Soc. 127(1999),  3533-3545.

This article is available in PostScript format.


On oscillatory integral operators with folding

canonical relations

by Allan Greenleaf and Andreas Seeger

appeared in Studia Mathematica 132(2) (1999), 125-139.


Fourier integral operators with cusp singularities

by Allan Greenleaf and Andreas Seeger

appeared in: American Journal of Mathematics 120 (1998), 1077-1119.


Acknowledgment and Disclaimer This material is based upon work supported by the National Science Foundation under various grants, including DMS-9877101, DMS-0138167, DMS-0551894 and DMS-0853892. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Preprints may differ from final published versions.

This page was last revised on December 12, 2010.