Almut Burchard -- publications  




Almut Burchard

Research interests:
Geometric problems in functional analysis, PDE and probability
Symmetrization, sharp inequalities, non-local functionals
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 (M.S. thesis, in German), Universität Heidelberg, 1989

Articles in mathematics journals, including submissions

  1. "Nonlocal shape optimization via interactions of attractive and repulsive potentials", with Rustum Choksi and Ihsan Topaloglu
    15 pages. Indiana University Mathematics Journal (to appear)    [arXiv:1512.07282]

  2. "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)    [arXiv:1509.02454]

  3. "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]

  4. "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]

  5. "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]

  6. "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]

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

  8. "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]

  9. "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, preprint, arXiv:0905.1834]

  10. "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]

  11. "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]

  12. "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]

  13. "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]

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

  15. "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]

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

  17. "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]

  18. "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]

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

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

  21. "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]

  22. "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]

Other articles
  1. "Window flow control systems with random service", Alireza Shekaramiz, Jörg Liebeherr, and AB
    35 pages (July 2015)    [arXiv:1507.04631]

  2. "Network-layer performance analysis of multihop fading channels", Hussein al-Zubaidy, Jörg Liebeherr, and AB
    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]

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

  4. "Delay bounds in communication networks with heavy-tailed and self-similar traffic", Jörg Liebeherr, AB, 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]

  5. "On the impact of link scheduling on end-to-end delays in large networks, Jörg Liebeherr, Y. Ghiassi-Farrokhfal, and AB
    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]

  6. "On superlinear scaling of network delays", AB, 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]

  7. "Scaling properties of statistical end-to-end bounds in the network calculus", Florin Ciucu, AB, 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", Best Student Paper Award, ACM Sigmetrics 2005, 2300-2312     [DOI 10.1145/1064212.1064251, preprint]

  8. "A network calculus with effective bandwidth", Chengzhi Li, AB, 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]

  9. "A min-plus calculus for end-to-end statistical service guarantees", AB, 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.     [arXiv.cs/0205001]

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

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

  12. "Statistical service assurances for traffic scheduling algorithms", Robert Boorstyn, AB, 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]

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

  14. "A linear-time online task assignment scheme for multiprocessor systems", AB, 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]

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