hhead>
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)
- "On monotonicity of heat kernels: a new example and counterexamples",
with A`ngel D. Marti&\grave;nez
Transactions of the American Mathematical Society (to appear)
(to appear)
[arXiv:2502.08212]
- "Maximizers of nonlocal interactions of Wasserstein type",
with Davide Carazzato and Ihsan Topaloglu
ESAIM: Control, Optimisation and Calculus of Variations
(to appear)
[arXiv:2309.05522]
- "Vanishing mean oscillation and continuity of
rearrangements",
with Galia Dafni and Ryan Gibara
Advances in Mathematics 437, Paper No. 109379
(February 2024)
[arXiv:2201.05130]
- "Extendability and the
∂
operator on the Hartogs triangle",
with Joshua Flynn, Guozhen Lu, and Mei-Chi Shaw
Mathematische Zeitschrift 301:2771-2792 (2022)
[arXiv:2106.09867]
- "Mean oscillation bounds on rearrangements",
with Galia Dafni and Ryan Gibara
Transactions of the AMS 375:4429-4444 (2022)
[arXiv:2011.09111v2]
- "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]
- "A stability result for Riesz potentials in higher dimensions",
with Gregory R. Chambers
Submitted August 2020. Preprint 18 pages
[arXiv:2007.11664]
- "Steiner symmetrization along a certain equidistributed sequence of
directions", with Reza Asad
Preprint 8 pages (September 2015; posted May 2020)
[arXiv:2005.13597]
- "Near-pulse solutions of the FitzHugh-Nagumo equations
on cylindrical surfaces",
with Afroditi Talidou and Israel Michael Sigal
Journal of Nonlinear Science 31:57, 39 pages (2021)
[arXiv:2004.06878]
- "On the strong attraction limit for a class of
nonlocal interaction energies", with Rustum Choksi and
Elias Hess-Childs
Nonlinar Analysis 198:111844, 12 pages (2020)
[DOI 10.1016/j.na.2020.111844,
arXiv:1911.02539]
-
"A general per-flow service curve for GPS", with Jörg Liebeherr
NetCal workshop at ITC-30, 2018.
Preprint 16 pages
[arXiv:1804.08034]
-
"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]
- "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]
- "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]
-
"Window flow control systems with random service",
with Alireza Shekaramiz and Jörg Liebeherr
Preprint 35 pages (2015)
[arXiv:1507.04631]
- "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]
- "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]
- "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]
-
"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]
- "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]
- "Random polarizations", with
Marc Fortier
Advances in Mathematics 334:550-573 (2013)
[DOI 10.1016/j.aim.2012.10.010,
arXiv:1104.4103]
-
"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]
- "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]
- "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]
-
"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]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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]
- "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
- "Compactness via symmetrization", with Yan Guo
Journal of Functional Analysis 214:40-73 (2004)
[DOI 10.1016/j.jfa.2004.04.005,
preprint]
- "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]
- "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]
- "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]
- "Comparison theorems for exit times", with Michael Schmuckenschläger
Geometric and Functional Analysis 11:651-692 (2001)
[DOI 10.1007/PL00001681,
preprint]
- "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]
- "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]
- "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]
- "Steiner symmetrization is continuous in W(1,p)"
Geometric and Functional Analysis 7:823-860 (1997)
[DOI 10.1007/s000390050027,
preprint]
- "Cases of equality in the Riesz rearrangement inequality"
Annals of Mathematics (2) 143:499-527 (1996)
[JSTOR,
preprint]
- "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]
-
"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]
- "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]
-
"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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