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Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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A variational characterization of condenser capacities in $C^n$ within a class of plurisubharmonic functions

100%
Kalina J.
Annales Polonici Mathematici
|
1983
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tom 41
|
nr 2
167-173
2
Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik
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Foliations by complex manifolds involving the complex Hessian

90%
Ławrynowicz J., Kalina J., Okada M.
Instytut Matematyczny Polskiej Akademii Nauk
EN
CONTENTS Summary...................................................................................................................................................................3 1. Introduction and an outline of results....................................................................................................................5 2. Capacities on complex manifolds and the generalized complex Monge-Ampère equations..................................8 3. Foliations............................................................................................................................................................10 4. Proof of the existence theorem in the holomorphically decomposable case.......................................................12 5. Proof of the existence theorem in the exterior product case...............................................................................14 6. Natural Markov processes connected with the foliation $ℒ_{k+p-1}$.................................................................16 7. Properties of canonical diffusions.......................................................................................................................18 8. Laplace-Beltrami operator on Riemannian manifolds.........................................................................................21 9. Harmonic theory on compact complex manifolds................................................................................................23 10. Laplace-Beltrami operator as the generator of a canonical diffusion................................................................27 11. Laplace-Beltrami operator in the case of the sphere and the hyperboloid........................................................29 12. Complex Hessian involving convex functions....................................................................................................33 13. Some examples of applications.........................................................................................................................36 14. Hypersurfaces in ℂ³ depending on two holomorphic functions.........................................................................41 References.............................................................................................................................................................43
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Weitzenböck Formula on Lie Algebroids

82%
Balcerzak B., Kalina J., Pierzchalski A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2012
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tom 60
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nr 2
165-176
EN
A Weitzenböck formula for the Laplace-Beltrami operator acting on differential forms on Lie algebroids is derived.
4
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Weitzenböck Formula for SL(q)-foliations

82%
Bartoszek A., Kalina J., Pierzchalski A.
Bulletin of the Polish Academy of Sciences. Mathematics
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2010
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tom 58
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nr 2
179-188
EN
A Weitzenböck formula for SL(q)-foliations is derived. Its linear part is a relative trace of the relative curvature operator acting on vector valued forms.
5
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Only one of generalized gradients can be elliptic

82%
Kalina J., Pierzchalski A., Walczak P.
Annales Polonici Mathematici
|
1997
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tom 67
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nr 2
111-120
EN
Decomposing the space of k-tensors on a manifold M into the components invariant and irreducible under the action of GL(n) (or O(n) when M carries a Riemannian structure) one can define generalized gradients as differential operators obtained from a linear connection ∇ on M by restriction and projection to such components. We study the ellipticity of gradients defined in this way.
6
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The global Yang-Mills equations depending on an arbitrary metric

82%
Gaveau B., Kalina J., Lawrynowicz J., Wojtczak L.
Annales Polonici Mathematici
|
1985
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tom 46
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nr 1
105-114
7
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Biholomorphic invariance of capacity and the capacity of an annulus

80%
Kalina J.
Annales Polonici Mathematici
|
1983
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tom 41
|
nr 2
175-183
8
Content available remote

Foliations and the generalized complex Monge-Ampère equations

71%
Kalina J., Ławrynowicz J.
Banach Center Publications
|
1983
|
tom 11
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nr 1
111-119
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