Spencer D C. Overdetermined systems of linear partial differential equations[J]. Bulletin of the American Mathematical Society, 1969, 75(2): 179-239.
2
J J Kohn. Subellipticity of the $$\bar \partial$$ -Neumann problem on pseudo-convex domains: Sufficient conditionsproblem on pseudo-convex domains: Sufficient conditions. 1979.
3
Folland G B. The tangential Cauchy-Riemann complex on spheres[J]. Transactions of the American Mathematical Society, 1972: 83-133.
4
Golubitsky O, Kondratieva M V, Ovchinnikov A, et al. A Bound for Orders in Differential Nullstellensatz[J]. Journal of Algebra, 2008, 322(11): 3852-3877.
5
Munoz J, Muriel F, Rodriguez J C, et al. A remark on Goldschmidt\u0027s theorem on formal integrability[J]. Journal of Mathematical Analysis and Applications, 2001, 254(1): 275-290.
6
Makhlouf Derridj. Ingalits priori et estimation sous-elliptique pour $$\bar \partial $$ dans des ouverts non pseudoconvexes. 1980.
7
W J Sweeney. A condition for subellipticity in Spencer's Neumann problem. 1976.
8
Mackichan B. A generalization to overdetermined systems of the notion of diagonal operators[J]. Acta Mathematica, 1971.
9
Derridj M. Domaines a estimation maximale[J]. Mathematische Zeitschrift, 1991, 208(1): 92-100.
10
Samborskii S N. Coercive boundary-value problems for overdetermined systems (parabolic problems)[J]. Ukrainian Mathematical Journal, 1985, 36(4): 385-390.
M. GrüterDüsseldorf University, Düsseldorf, West GermanyS. HildebrandtBonn University, Bonn, West GermanyJ. C. C. NitscheUniversity of Minnesota, Minneapolis, MN, USA
Michael Struwe. The existence of surfaces of constant mean curvature with free boundaries. 1988.
2
Ros A, Vergasta E. Stability for hypersurfaces of constant mean curvature with free boundary[J]. Geometriae Dedicata, 1995, 56(1): 19-33.
3
Grter M. Boundary regularity for solutions of a partitioning problem[J]. Archive for Rational Mechanics and Analysis, 1987, 97(3).
4
Kekicheff P. From Cylinders to Bilayers: A Structural Study of Phase Transformations in a Lyotropic Liquid Crystal[J]. Molecular Crystals and Liquid Crystals, 2006, 198(1): 131-144.
5
Gruter M. The monotonicity formula in geometric measure theory, and an application to a partially free boundary problem[C]., 1988: 238-255.
6
Fall M M. EMBEDDED DISC-TYPE SURFACES WITH LARGE CONSTANT MEAN CURVATURE AND FREE BOUNDARIES[J]. Communications in Contemporary Mathematics, 2012, 14(06).
7
Grter M. Boundary regularity for solutions of a partitioning problem[J]. Archive for Rational Mechanics and Analysis, 1987, 97(3).
8
Burger W, Kuwert E. Area-minimizing disks with free boundary and prescribed enclosed volume[J]. Crelle\u0027s Journal, 2008, 2008(621): 1-27.
9
Frank Muller. Hölder continuity of surfaces with bounded mean curvature at corners where Plateau boundaries meet free boundaries. 2005.
10
Frank Muller. On stable surfaces of prescribed mean curvature with partially free boundaries. 2005.
We extend our family rigidity and vanishing theorems in [{\bf LiuMaZ}] to the Spin^ c case. In particular, we prove a K-theory version of the main results of [{\bf H}],[{\bf Liu1}, Theorem B] for a family of almost complex manifolds.
We introduce new finite-dimensional cohomologies on symplectic manifolds. Each exhibits Lefschetz decomposition and contains
a unique harmonic representative within each class. Associated with each cohomology is a primitive cohomology defined purely
on the space of primitive forms. We identify the dual currents of lagrangians and more generally coisotropic submanifolds with elements
of a primitive cohomology, which dualizes to a homology on coisotropic chains.