Almut Burchard -- publications  




Almut Burchard

Research interests:
Geometric problems in functional analysis, PDE and probability
Symmetrization, sharp inequalities, non-local functionals, aggregation
Network calculus

Theses and notes

"How to achieve radial symmetry through simple rearrangements".
CMS Notes 44(5):16-17 (October/November 2012) [PDF]

"Rearrangement inequalities"
47 pages. Lecture notes, June 2009 [PDF, Corrections]

"Cases of equality in the Riesz rearrangement inequality", supervised by Michael Loss
84 pages. Ph.D. thesis, Georgia Institute of Technology, 1994 [PDF]

"Ein Chemostat-Modell für den Abbau eines komplexen Substrats durch eine symbiotische Assoziation zweier Spezies", supervised by Willi Jäger
92 pages. Diplomarbeit (Master's thesis, in German), Universität Heidelberg, 1989

Articles (including submissions and preprints)

  1. "Vanishing mean oscillation and continuity of rearrangements", with Galia Dafni and Ryan Gibara
    Submitted January 2022. Preprint 21 pages    [arXiv:2201.05130]

  2. "Extendability and the operator on the Hartogs triangle", with Joshua Flynn, Guozhen Lu, and Mei-Chi Shaw
    Accepted for publication by Mathematische Zeitschrift (January 2022). Preprint 23 pages    [arXiv:2106.09867]

  3. "Mean oscillation bounds on rearrangements", with Galia Dafni and Ryan Gibara
    Transactions of the AMS (online first; February 2022). Preprint 17 pages    [arXiv:2011.09111v2]

  4. "A note on decreasing rearrangement and mean oscillation on measure spaces", with Galia Dafni and Ryan Gibara
    Proceedings of the AMS 149(10): 4341-4354 (2021).    [arXiv:2010.15024]

  5. "A stability result for Riesz potentials in higher dimensions", with Gregory R. Chambers
    Submitted August 2020. Preprint 18 pages    [arXiv:2007.11664]

  6. "Steiner symmetrization along a certain equidistributed sequence of directions", with Reza Asad
    Preprint 8 pages (September 2015; posted May 2020)     [arXiv:2005.13597]

  7. "Near-pulse solutions of the FitzHugh-Nagumo equations on cylindrical surfaces", with Afroditi Talidou and Israel Michael Sigal
    Journal of Nonlinear Science, to appear. Preprint 37 pages    [arXiv:2004.06878]

  8. "On the strong attraction limit for a class of nonlocal interaction energies", with Rustum Choksi and Elias Hess-Childs
    Nonlinar Analysis 198, Paper # 111844, 12 pages (online April 2020)    [DOI 10.1016/, arXiv:1911.02539]

  9. "A general per-flow service curve for GPS", with Jörg Liebeherr
    NetCal workshop at ITC-30, 2018. Preprint 16 pages    [arXiv:1804.08034]

  10. "Analysis of a queueing model for energy storage systems with self-discharge", with Majid Raeis and Jörg Liebeherr
    ACM Transactions on Modeling and Performance Evaluation of Computing Systems (TOMPECS) 5(3), 26 pages (online November 2020).    [DOI 10.1145/3422711, arXiv:1710.09506]

  11. "Nonlocal shape optimization via interactions of attractive and repulsive potentials", with Rustum Choksi and Ihsan Topaloglu
    Indiana University Mathematics Journal 67(1):375-395 (2018)    [DOI 10.151iiiiiii2/iumj.2018.67.6234, arXiv:1512.07282]

  12. "Ergodic properties of folding maps on spheres", with Gregory R. Chambers and Anne Dranovski
    Discrete and Continuous Dynamical Systems, Series A 37(3):1183-1200 (2017)    [DOI 10.3934/dcds.2017049, arXiv:1509.02454]

  13. "Window flow control systems with random service", with Alireza Shekaramiz and Jörg Liebeherr
    Preprint 35 pages (2015)    [arXiv:1507.04631]

  14. "On the extremals of the Pólya-Szegő inequality", with Adele Ferone
    Indiana University Mathematics Journal 64(5):1447-1463 (2015)    [DOI 10.1512/iumj.2015.64.5652, arXiv:1407.6567]

  15. "Geometric stability of the Coulomb energy", with Gregory R. Chambers
    Calculus of Variations and PDE 54(3):3241-3250 (2015)    [DOI 10.1007/s00526-015-0900-8, arXiv:1407.1918]

  16. "Perimeter under multiple Steiner symmetrizations", with Gregory R. Chambers
    Journal of Geometric Analysis 25(2):871-882 (2015)     [DOI 10.1007/s12220-013-9448-z, arXiv:1209.4521]

  17. "Network-layer performance analysis of multihop fading channels", with Hussein al-Zubaidy and Jörg Liebeherr
    ACM/IEEE Transactions on Networking 24:204-217 (2016)    [DOI 10.1109/TNET.2014.2360675, arXiv:1207.6630]
    Conference version: "A (min,×) network calculus for multi-hop fading channels". IEEE Infocom 2013, 1833-1841     [DOI 10.1109/INFCOM.2013.6566982]

  18. "Convergence in shape of Steiner symmetrizations", with Gabriele Bianchi, Paolo Gronchi, and Aljoša Volčič
    Indiana University Mathematics Journal 61(4):1695-1710 (2012)     [DOI 10.1512/iumj.2012.61.5087, arXiv:1206.2041]

  19. "Random polarizations", with Marc Fortier
    Advances in Mathematics 334:550-573 (2013)     [DOI 10.1016/j.aim.2012.10.010, arXiv:1104.4103]

  20. "The impact of link scheduling on long paths: Statistical analysis and optimal bounds", with Jörg Liebeherr and Yashar Ghiassi-Farrokhfal
    IEEE Infocom 2011, 1242-1259     [DOI 10.1109/INFCOM.2011.5934905]
    Preprint 20 pages "Statistical analysis of link scheduling on long paths" (2011)    [arXiv:1101.1237]

  21. "Convergence to equilibrium for a thin-film equation on a cylindrical surface", with Marina Chugunova and Benjamin K. Stephens
    Communications in PDE 37: 585-609 (2012)     [DOI 10.1080/03605302.2011.648704, arXiv:1011.2108]
    Early version (14 pages): "On the energy-minimizing steady states of a thin film equation" (2010)    [arXiv:1009.4092]

  22. "Delay bounds in communication networks with heavy-tailed and self-similar traffic", with Jörg Liebeherr and Florin Ciucu
    IEEE Transactions on Information Theory 58:1010-1024 (2012)     [DOI 10.1109/TIT.2011.2173713, arXiv:0911.3856]
    Conference version: "Non-asymptotic delay bounds for networks with heavy-tailed traffic". IEEE Infocom 2010, 1-9     [DOI 10.1109/INFCOM.2010.5461913]

  23. "On the impact of link scheduling on end-to-end delays in large networks, with Jörg Liebeherr and Yashar Ghiassi-Farrokhfal
    IEEE Journal on Selected Areas in Communications, Special Issue on Trading Rate for Delay at the Transport and Application Layers, 29:1009-1020 (2011)     [DOI 10.1109/JSAC.2011.110511]
    Conference version: "Does link scheduling matter on long paths?" ICDCS 2010, 199-208     [DOI 10.1109/ICDCS.2010.62]

  24. "On superlinear scaling of network delays", with Jörg Liebeherr and Florin Ciucu
    ACM/IEEE Transactions on Networking, 19:1043-1056 (2011)     [DOI 10.1109/TNET.2010.2095505, preprint]
    Conference version: "On Θ(H log H) scaling of network delays". IEEE Infocom 2007, 1866-1874     [DOI 10.1109/INFCOM.2007.217]

  25. "On computing the instability index of a non-selfadjoint differential operator associated with coating and rimming flows", with Marina Chugunova
    SIAM Journal on Mathematical Analysis 43:367-388 (2011)     [DOI 10.1137/090759495, arXiv:0905.1834]

  26. "Explicit Yamabe flow of an asymmetric cigar", with Robert McCann and Aaron Smith
    Methods and Applications of Analysis 15:65-80 (2008)     [Project Euclid, preprint]

  27. "A network calculus with effective bandwidth", with Chengzhi Li and Jörg Liebeherr
    IEEE/ACM Transaction on Networking 15(6):1442-1453 (2007)     [DOI 10.1109/TNET.2007.896501]
    Early version: University of Virginia Technical Report CS-2003-20   [preprint]

  28. "Rearrangement inequalities for functionals with monotone integrands", with Hichem Hajaiej
    Journal of Functional Analysis 233:561-582 (2006)     [DOI 10.1016/j.jfa.2005.08.010, arXiv:0506.336]

  29. "On the geometry of optimal windows, with special focus on the square", with Jochen Denzler
    SIAM Journal on Mathematical Analysis 37:1800-1827 (2006)     [DOI 10.1137/S0036141004444184, preprint]

  30. "Scaling properties of statistical end-to-end bounds in the network calculus",with Florin Ciucu and Jörg Liebeherr
    IEEE Transactions on Information Theory 52:2300-2312 (2006)     [DOI 10.1109/TIT.2006.874380]
    Conference version: "A network service curve approach for the stochastic analysis of networks",
    ACM Sigmetrics 2005, 2300-2312 (Best Student Paper Award)     [DOI 10.1145/1064212.1064251, preprint]

  31. "On an isoperimetric inequality for a Schrödinger operator depending on the curvature of a loop", with Lawrence E. Thomas
    Journal of Geometric Analysis 15:543-563 (2005)     [DOI 10.1007/BF02922244, arXiv:0505123]

  32. "A min-plus calculus for end-to-end statistical service guarantees", with Jörg Liebeherr and Stephen D. Patek
    IEEE Transactions on Information Theory 52:4105-4114 (2006)     [DOI 10.1109/TIT.2006.880019, preprint]
    Early version: "A calculus for end-to-end statistical service guarantees", University of Virginia Technical Report CS-2001-19

  33. "Compactness via symmetrization", with Yan Guo
    Journal of Functional Analysis 214:40-73 (2004)     [DOI 10.1016/j.jfa.2004.04.005, preprint]

  34. "On the Cauchy problem for a dynamical Euler's elastica", with Lawrence E. Thomas
    Communications in PDE 28:271-300 (2003)     [DOI 10.1081/PDE-120019382, arXiv:0202278]

  35. "Statistical per-flow service bounds in a network with aggregate provisioning", with Jörg Liebeherr and Stephen D. Patek
    IEEE Infocom 2003, 1680-1690     [DOI 10.1109/INFCOM.2003.1209191, preprint]

  36. "Confocal FRET microscopy to measure clustering of receptor-ligand complexes in endocytic membranes", with Horst Wallrabe, Masilamani Elangovan, Ammasi Periasamy, and Margarida Barroso
    Biophysical Journal 85:1-13 (2003)     [DOI 10.1016/S0006-3495(03)74500-7, preprint]
    Announcement: Proc. SPIE 2002, 9 pages (non-refereed)     [preprint]

  37. "Comparison theorems for exit times", with Michael Schmuckenschläger
    Geometric and Functional Analysis 11:651-692 (2001)     [DOI 10.1007/PL00001681, preprint]

  38. "Statistical service assurances for traffic scheduling algorithms", with Robert Boorstyn, Jörg Liebeherr, and Chaiwat Oottamakorn
    Journal for Selected Areas in Communications 18:2651-2664 (2000)     [DOI 10.1109/49.898747, preprint]
    Conference version: "Effective envelopes: statistical bounds on multiplexed traffic in packet networks", IEEE Infocom 2000     [DOI 10.1109/INFCOM.2000.832502, preprint]

  39. "Scaling limits for minimal and random spanning trees in two dimensions", with Michael Aizenman, Charles M. Newman, and David B. Wilson
    Random Structures and Algorithms 15:319-367 (1999)     [DOI 10.1002/(SICI)1098-2418(199910/12)15:3/4<319::AID-RSA8>3.0.CO;2-G, arXiv:9809145]

  40. "Hölder regularity and dimension bounds for random curves", with Michael Aizenman
    Duke Mathematial Journal 99:419-453 (1999)     [DOI 10.1215/S0012-7094-99-09914-3, arXiv:9801027]

  41. "Steiner symmetrization is continuous in W(1,p)"
    Geometric and Functional Analysis 7:823-860 (1997)     [DOI 10.1007/s000390050027, preprint]

  42. "Cases of equality in the Riesz rearrangement inequality"
    Annals of Mathematics (2) 143:499-527 (1996)     [JSTOR, preprint]

  43. "New strategies for assigning real-time tasks to multiprocessor systems", with Jörg Liebeherr, Yingfeng Oh, and Sang H. Son
    IEEE Transactions on Computers 44:1429-1442 (1995)     [DOI 10.1109/12.477248, preprint]

  44. "Substrate degradation by a mutualistic association of two species in the chemostat"
    Journal of Mathematical Biology 32:465-489 (1994)     [DOI 10.1007/BF00160169, preprint]

  45. "A linear-time online task assignment scheme for multiprocessor systems", with Jörg Liebeherr, Yingfeng Oh, and Sang H. Son
    Proc. 11th IEEE Workshop on Real-Time Operating Systems and Software, 28-31 (Seattle, 1994)     [DOI 10.1109/RTOSS.1994.292566, preprint]

  46. "Smooth conjugacy of center manifolds", with Bo Deng and Kening Lu
    Proceedings of the Royal Society of Edinburgh, Section A 120:61-77 (1992)     [DOI 10.1017/S0308210500014980, preprint]

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