Recent Issues
Volume 28, 2 issues
Volume 28
Issue 2, 497–1003
Issue 1, 1–496
Volume 27, 9 issues
Volume 27
Issue 9, 3387–3831
Issue 8, 2937–3385
Issue 7, 2497–2936
Issue 6, 2049–2496
Issue 5, 1657–2048
Issue 4, 1273–1655
Issue 3, 823–1272
Issue 2, 417–821
Issue 1, 1–415
Volume 26, 8 issues
Volume 26
Issue 8, 3307–3833
Issue 7, 2855–3306
Issue 6, 2405–2853
Issue 5, 1907–2404
Issue 4, 1435–1905
Issue 3, 937–1434
Issue 2, 477–936
Issue 1, 1–476
Volume 25, 7 issues
Volume 25
Issue 7, 3257–3753
Issue 6, 2713–3256
Issue 5, 2167–2711
Issue 4, 1631–2166
Issue 3, 1087–1630
Issue 2, 547–1085
Issue 1, 1–546
Volume 24, 7 issues
Volume 24
Issue 7, 3219–3748
Issue 6, 2675–3218
Issue 5, 2149–2674
Issue 4, 1615–2148
Issue 3, 1075–1614
Issue 2, 533–1073
Issue 1, 1–532
Volume 23, 7 issues
Volume 23
Issue 7, 3233–3749
Issue 6, 2701–3231
Issue 5, 2165–2700
Issue 4, 1621–2164
Issue 3, 1085–1619
Issue 2, 541–1084
Issue 1, 1–540
Volume 22, 7 issues
Volume 22
Issue 7, 3761–4380
Issue 6, 3145–3760
Issue 5, 2511–3144
Issue 4, 1893–2510
Issue 3, 1267–1891
Issue 2, 645–1266
Issue 1, 1–644
Volume 21, 6 issues
Volume 21
Issue 6, 3191–3810
Issue 5, 2557–3190
Issue 4, 1931–2555
Issue 3, 1285–1930
Issue 2, 647–1283
Issue 1, 1–645
Volume 20, 6 issues
Volume 20
Issue 6, 3057–3673
Issue 5, 2439–3056
Issue 4, 1807–2438
Issue 3, 1257–1806
Issue 2, 629–1255
Issue 1, 1–627
Volume 19, 6 issues
Volume 19
Issue 6, 3031–3656
Issue 5, 2407–3030
Issue 4, 1777–2406
Issue 3, 1155–1775
Issue 2, 525–1154
Issue 1, 1–523
Volume 18, 5 issues
Volume 18
Issue 5, 2487–3110
Issue 4, 1865–2486
Issue 3, 1245–1863
Issue 2, 617–1244
Issue 1, 1–616
Volume 17, 5 issues
Volume 17
Issue 5, 2513–3134
Issue 4, 1877–2512
Issue 3, 1253–1876
Issue 2, 621–1252
Issue 1, 1–620
Volume 16, 4 issues
Volume 16
Issue 4, 1881–2516
Issue 3, 1247–1880
Issue 2, 625–1246
Issue 1, 1–624
Volume 15, 4 issues
Volume 15
Issue 4, 1843–2457
Issue 3, 1225–1842
Issue 2, 609–1224
Issue 1, 1–607
Volume 14, 5 issues
Volume 14
Issue 5, 2497–3000
Issue 4, 1871–2496
Issue 3, 1243–1870
Issue 2, 627–1242
Issue 1, 1–626
Volume 13, 5 issues
Volume 13
Issue 5, 2427–3054
Issue 4, 1835–2425
Issue 3, 1229–1833
Issue 2, 623–1227
Issue 1, 1–621
Volume 12, 5 issues
Volume 12
Issue 5, 2517–2855
Issue 4, 1883–2515
Issue 3, 1265–1882
Issue 2, 639–1263
Issue 1, 1–637
Volume 11, 4 issues
Volume 11
Issue 4, 1855–2440
Issue 3, 1255–1854
Issue 2, 643–1254
Issue 1, 1–642
Volume 10, 4 issues
Volume 10
Issue 4, 1855–2504
Issue 3, 1239–1853
Issue 2, 619–1238
Issue 1, 1–617
Volume 9, 4 issues
Volume 9
Issue 4, 1775–2415
Issue 3, 1187–1774
Issue 2, 571–1185
Issue 1, 1–569
Volume 8, 3 issues
Volume 8
Issue 3, 1013–1499
Issue 2, 511–1012
Issue 1, 1–509
Volume 7, 2 issues
Volume 7
Issue 2, 569–1073
Issue 1, 1–568
Volume 6, 2 issues
Volume 6
Issue 2, 495–990
Issue 1, 1–494
Volume 5, 2 issues
Volume 5
Issue 2, 441–945
Issue 1, 1–440
Volume 4, 1 issue
Volume 3, 1 issue
Volume 2, 1 issue
Volume 1, 1 issue
1
D R Adams ,
A
note on Riesz potentials , Duke Math. J. 42 (1975) 765
MR458158
2
F J Almgren Jr. ,
The
homotopy groups of the integral cycle groups , Topology
1 (1962) 257 MR146835
3
F J Almgren Jr. ,
The theory of varifolds , mimeographed notes (1965)
4
J Chen , G Tian ,
Compactification of
moduli space of harmonic mappings , Comment. Math. Helv.
74 (1999) 201 MR1691947
5
R Coifman , P L
Lions , Y Meyer , S Semmes , Compensated
compactness and Hardy spaces , J. Math. Pures Appl. 72
(1993) 247 MR1225511
6
T H Colding ,
W P Minicozzi II , Width and finite
extinction time of Ricci flow , Geom. Topol. 12 (2008)
2537 MR2460871
7
T H Colding ,
W P Minicozzi II , Width and mean
curvature flow , Geom. Topol. 12 (2008) 2517 MR2460870
8
R Courant , Dirichlet’s
principle, conformal mapping, and minimal surfaces ,
Springer (1977) MR0454858
9
R Courant , N
Davids , Minimal surfaces
spanning closed manifolds , Proc. Nat. Acad. Sci. U.S.A.
26 (1940) 194 MR1472
10
C De Lellis , J
Ramic , Min-max
theory for minimal hypersurfaces with boundary , Ann.
Inst. Fourier (Grenoble) 68 (2018) 1909 MR3893761
11
W Ding , J Li ,
Q Liu , Evolution of
minimal torus in Riemannian manifolds , Invent. Math.
165 (2006) 225 MR2231956
12
W Ding , G Tian ,
Energy
identity for a class of approximate harmonic maps from
surfaces , Comm. Anal. Geom. 3 (1995) 543 MR1371209
13
L C Evans ,
Partial
differential equations , 19, Amer. Math. Soc. (2010)
MR2597943
14
A M Fraser ,
On
the free boundary variational problem for minimal
disks , PhD thesis, Stanford University (1998) MR2698288
15
A M Fraser ,
On the free boundary variational problem for minimal
disks , Comm. Pure Appl. Math. 53 (2000) 931 MR1755947
16
A Fraser , R
Schoen , The first Steklov
eigenvalue, conformal geometry, and minimal surfaces ,
Adv. Math. 226 (2011) 4011 MR2770439
17
A Fraser , R
Schoen , Sharp eigenvalue
bounds and minimal surfaces in the ball , Invent. Math.
203 (2016) 823 MR3461367
18
L Grafakos ,
Modern
Fourier analysis , 250, Springer (2009) MR2463316
19
M Grüter , J
Jost , On
embedded minimal disks in convex bodies , Ann. Inst. H.
Poincaré Anal. Non Linéaire 3 (1986) 345 MR868522
20
F Hélein , Harmonic maps,
conservation laws and moving frames , 150, Cambridge
Univ. Press (2002) MR1913803
21
J Hohrein ,
Existence of unstable minimal surfaces of higher genus in
manifolds of nonpositive curvature , PhD thesis, Universität
Heidelberg (1994)
22
R A Hunt , On
L ( p, q ) spaces ,
Enseign. Math. 12 (1966) 249 MR223874
23
T Iwaniec , G
Martin ,
Geometric function theory and non-linear analysis ,
Oxford Univ. Press (2001) MR1859913
24
J Jost , Existence
results for embedded minimal surfaces of controlled topological
type, II , Ann. Scuola Norm. Sup. Pisa Cl. Sci. 13
(1986) 401 MR881099
25
J Jost ,
Two-dimensional geometric variational problems , Wiley
(1991) MR1100926
26
J Jost , L Liu ,
M Zhu , The qualitative
behavior at the free boundary for approximate harmonic maps
from surfaces , Math. Ann. 374 (2019) 133 MR3961307
27
T Lamm , L Lin ,
Estimates
for the energy density of critical points of a class of
conformally invariant variational problems , Adv. Calc.
Var. 6 (2013) 391 MR3199733
28
P Laurain , Analyse des problèmes
conformément invariants , from: "Séminaire Laurent
Schwartz–Équations aux dérivées partielles et applications,
2016–2017" (editors F Golse, F Merle), Ed. Éc. Polytech. (2017)
MR3790939
29
P Laurain , L
Lin , Energy convexity of intrinsic bi-harmonic maps and
applications, I: Spherical target , preprint (2018) arXiv:1805.09428
30
P Laurain , R
Petrides , Regularity and
quantification for harmonic maps with free boundary ,
Adv. Calc. Var. 10 (2017) 69 MR3592578
31
M Li , X Zhou ,
Min-max theory for free boundary minimal hypersurfaces, I:
Regularity theory , preprint (2016) arXiv:1611.02612
32
F C Marques , A
Neves , Min-max theory of
minimal surfaces and applications , from: "Mathematical
Congress of the Americas" (editors J A de la Peña,
J A López-Mimbela, M Nakamura, J Petean), Contemp. Math.
656, Amer. Math. Soc. (2016) 13 MR3457593
33
R Montezuma , A
mountain pass theorem for minimal hypersurfaces with fixed
boundary , preprint (2018) arXiv:1802.04757
34
M Morse , C
Tompkins , The
existence of minimal surfaces of general critical
types , Ann. of Math. 40 (1939) 443 MR1503471
35
F Müller , A
Schikorra , Boundary regularity
via Uhlenbeck–Rivière decomposition , Analysis
( Munich) 29 (2009) 199 MR2554638
36
T H Parker ,
Bubble tree
convergence for harmonic maps , J. Differential Geom. 44
(1996) 595 MR1431008
37
T H Parker ,
J G Wolfson , Pseudo-holomorphic maps
and bubble trees , J. Geom. Anal. 3 (1993) 63 MR1197017
38
S Poornima , An
embedding theorem for the Sobolev space W 1 , 1 , Bull.
Sci. Math. 107 (1983) 253 MR719267
39
J Qing , Boundary regularity of
weakly harmonic maps from surfaces , J. Funct. Anal. 114
(1993) 458 MR1223710
40
J Qing , G Tian ,
Bubbling of the heat flows for harmonic maps from
surfaces , Comm. Pure Appl. Math. 50 (1997) 295 MR1438148
41
T Rivière , Conservation laws
for conformally invariant variational problems , Invent.
Math. 168 (2007) 1 MR2285745
42
T Rivière ,
Conformally invariant variational problems , preprint
(2012) arXiv:1206.2116
43
T Rivière , A viscosity method
in the min-max theory of minimal surfaces , Publ. Math.
Inst. Hautes Études Sci. 126 (2017) 177 MR3735867
44
T Rivière , M
Struwe , Partial regularity for
harmonic maps and related problems , Comm. Pure Appl.
Math. 61 (2008) 451 MR2383929
45
J Sacks , K
Uhlenbeck , The
existence of minimal immersions of 2 –spheres , Ann. of Math. 113 (1981) 1
MR604040
46
C Scheven , Partial regularity
for stationary harmonic maps at a free boundary , Math.
Z. 253 (2006) 135 MR2206640
47
B Sharp , Higher
integrability for solutions to a system of critical elliptic
PDE , Methods Appl. Anal. 21 (2014) 221 MR3251921
48
B Sharp , M Zhu ,
Regularity at the
free boundary for Dirac-harmonic maps from surfaces ,
Calc. Var. Partial Differential Equations 55 (2016) MR3465443
49
M Shiffman ,
The Plateau
problem for non-relative minima , Ann. of Math. 40
(1939) 834 MR467
50
L Simon ,
Lectures on geometric measure theory , 3, Aust. National
Univ. Centre for Mathematical Analysis (1983) MR756417
51
B Smyth , Stationary minimal
surfaces with boundary on a simplex , Invent. Math. 76
(1984) 411 MR746536
52
M Struwe , On a free boundary problem
for minimal surfaces , Invent. Math. 75 (1984) 547
MR735340
53
M Struwe ,
Plateau’s problem and the calculus of variations , 35,
Princeton Univ. Press (1988) MR992402
54
M Struwe , Variational
methods: applications to nonlinear partial differential
equations and Hamiltonian systems , 34, Springer (2008)
MR2431434
55
L Tartar ,
Imbedding theorems of Sobolev spaces into Lorentz
spaces , Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat.
1 (1998) 479 MR1662313
56
H C Wente ,
An
existence theorem for surfaces of constant mean
curvature , J. Math. Anal. Appl. 26 (1969) 318 MR243467
57
R Ye , On the existence of
area-minimizing surfaces with free boundary , Math. Z.
206 (1991) 321 MR1095757
58
X Zhou , On the existence of
min-max minimal torus , J. Geom. Anal. 20 (2010) 1026
MR2683775
59
X Zhou , On the free boundary
min-max geodesics , Int. Math. Res. Not. 2016 (2016)
1447 MR3509932
60
X Zhou , On the existence of
min-max minimal surface of genus g
≥ 2 , Commun. Contemp. Math. 19 (2017)
MR3665358