On the Monge-Ampere differential equation
B. N. Rachajsky (1969)
Matematički Vesnik
Similarity:
B. N. Rachajsky (1969)
Matematički Vesnik
Similarity:
Slimane Benelkourchi, Vincent Guedj, Ahmed Zeriahi (2008)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
Similarity:
Let be a compact Kähler manifold and be a smooth closed form of bidegree which is nonnegative and big. We study the classes of -plurisubharmonic functions of finite weighted Monge-Ampère energy. When the weight has fast growth at infinity, the corresponding functions are close to be bounded. We show that if a positive Radon measure is suitably dominated by the Monge-Ampère capacity, then it belongs to the range of the Monge-Ampère operator on some class . This is done by...
Sławomir Kołodziej (2003)
Annales Polonici Mathematici
Similarity:
regularity of the solutions of the complex Monge-Ampère equation in ℂPⁿ with the n-root of the right hand side in is proved.
Rafał Czyż (2010)
Annales Polonici Mathematici
Similarity:
Let Ω be a bounded hyperconvex domain in ℂn and let μ be a positive and finite measure which vanishes on all pluripolar subsets of Ω. We prove that for every continuous and strictly increasing function χ:(-∞,0) → (-∞,0) there exists a negative plurisubharmonic function u which solves the Monge-Ampère type equation . Under some additional assumption the solution u is uniquely determined.
Jean-Pierre Demailly, Sławomir Dinew, Vincent Guedj, Pham Hoang Hiep, Sławomir Kołodziej, Ahmed Zeriahi (2014)
Journal of the European Mathematical Society
Similarity:
Let be a compact Kähler manifold. We obtain uniform Hölder regularity for solutions to the complex Monge-Ampère equation on with right hand side, . The same regularity is furthermore proved on the ample locus in any big cohomology class. We also study the range of the complex Monge-Ampère operator acting on -plurisubharmonic Hölder continuous functions. We show that this set is convex, by sharpening Kołodziej’s result that measures with -density belong to and proving that...
Pham Hoang Hiep (2007)
Annales Polonici Mathematici
Similarity:
We study boundary values of functions in Cegrell’s class .
Matthew J. Gursky, Andrea Malchiodi (2015)
Journal of the European Mathematical Society
Similarity:
In this paper we consider Riemannian manifolds of dimension , with semi-positive -curvature and non-negative scalar curvature. Under these assumptions we prove (i) the Paneitz operator satisfies a strong maximum principle; (ii) the Paneitz operator is a positive operator; and (iii) its Green’s function is strictly positive. We then introduce a non-local flow whose stationary points are metrics of constant positive -curvature. Modifying the test function construction of Esposito-Robert,...
Pham Hoang Hiep (2006)
Annales Polonici Mathematici
Similarity:
We establish the comparison principle in the class . The result obtained is applied to the Dirichlet problem in .
Per Åhag, Rafał Czyż, Pham Hoàng Hiêp (2007)
Annales Polonici Mathematici
Similarity:
The energy class is studied for 0 < p < 1. A characterization of certain bounded plurisubharmonic functions in terms of and its pluricomplex p-energy is proved.
Urban Cegrell (2007)
Annales Polonici Mathematici
Similarity:
We show that if a decreasing sequence of subharmonic functions converges to a function in then the convergence is in .
Erwann Aubry, Colin Guillarmou (2011)
Journal of the European Mathematical Society
Similarity:
For odd-dimensional Poincaré–Einstein manifolds , we study the set of harmonic -forms (for ) which are (with ) on the conformal compactification of . This set is infinite-dimensional for small but it becomes finite-dimensional if is large enough, and in one-to-one correspondence with the direct sum of the relative cohomology and the kernel of the Branson–Gover [3] differential operators on the conformal infinity . We also relate the set of forms in the kernel of ...
Zdeněk Dušek (2015)
Czechoslovak Mathematical Journal
Similarity:
Let be a 4-dimensional Einstein Riemannian manifold. At each point of , the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor at . In this basis, up to standard symmetries and antisymmetries, just components of the curvature tensor are nonzero. For the space of constant curvature, the group acts as a transformation group between ST bases at and for the so-called 2-stein curvature tensors, the group acts as a transformation...
Tamalika Dutta, Nirabhra Basu, Arindam BHATTACHARYYA (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
In this paper we have studied conformal curvature tensor, conharmonic curvature tensor, projective curvature tensor in Lorentzian -Sasakian manifolds admitting conformal Ricci soliton. We have found that a Weyl conformally semi symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton is -Einstein manifold. We have also studied conharmonically Ricci symmetric Lorentzian -Sasakian manifold admitting conformal Ricci soliton. Similarly we have proved that a Lorentzian...
Neil Seshadri (2009)
Bulletin de la Société Mathématique de France
Similarity:
To any smooth compact manifold endowed with a contact structure and partially integrable almost CR structure , we prove the existence and uniqueness, modulo high-order error terms and diffeomorphism action, of an approximately Einstein ACH (asymptotically complex hyperbolic) metric on . We consider the asymptotic expansion, in powers of a special defining function, of the volume of with respect to and prove that the log term coefficient is independent of (and any choice...
Jerzy Kalina (1983)
Annales Polonici Mathematici
Similarity:
Mats Andersson, Elizabeth Wulcan (2014)
Annales de l’institut Fourier
Similarity:
Let be a coherent ideal sheaf on a complex manifold with zero set , and let be a plurisubharmonic function such that locally at , where is a tuple of holomorphic functions that defines . We give a meaning to the Monge-Ampère products for , and prove that the Lelong numbers of the currents at coincide with the so-called Segre numbers of at , introduced independently by Tworzewski, Gaffney-Gassler, and Achilles-Manaresi. More generally, we show that satisfy a certain...
Ernst Kuwert, Tobias Lamm, Yuxiang Li (2015)
Journal of the European Mathematical Society
Similarity:
For two-dimensional, immersed closed surfaces , we study the curvature functionals and with integrands and , respectively. Here is the second fundamental form, is the mean curvature and we assume . Our main result asserts that critical points are smooth in both cases. We also prove a compactness theorem for -bounded sequences. In the case of this is just Langer’s theorem [16], while for we have to impose a bound for the Willmore energy strictly below as an additional...
Shyamal Kumar Hui, Debabrata Chakraborty (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
The object of the present paper is to study -Ricci solitons on -Einstein -manifolds. It is shown that if is a recurrent torse forming -Ricci soliton on an -Einstein -manifold then is (i) concurrent and (ii) Killing vector field.
Sergey E. Stepanov, Irina I. Tsyganok, Marina B. Khripunova (2016)
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
Similarity:
In this paper we solve the problem of finding integrals of equations determining the Killing tensors on an -dimensional differentiable manifold endowed with an equiaffine -structure and discuss possible applications of obtained results in Riemannian geometry.
Régis Monneau, Jean-Michel Roquejoffre, Violaine Roussier-Michon (2013)
Annales scientifiques de l'École Normale Supérieure
Similarity:
We construct travelling wave graphs of the form , , , solutions to the -dimensional forced mean curvature motion () with prescribed asymptotics. For any -homogeneous function , viscosity solution to the eikonal equation , we exhibit a smooth concave solution to the forced mean curvature motion whose asymptotics is driven by . We also describe in terms of a probability measure on .
Najoua Gamara (2001)
Journal of the European Mathematical Society
Similarity:
Let be a compact CR manifold of dimension with a contact form , and its associated CR conformal laplacien. The CR Yamabe conjecture states that there is a contact form on conformal to which has a constant Webster curvature. This problem is equivalent to the existence of a function such that , on . D. Jerison and J. M. Lee solved the CR Yamabe problem in the case where and is not locally CR equivalent to the sphere of . In a join work with R. Yacoub, the CR Yamabe...
Yan Yan Li, Louis Nirenberg (2006)
Journal of the European Mathematical Society
Similarity:
A classical result of A. D. Alexandrov states that a connected compact smooth -dimensional manifold without boundary, embedded in , and such that its mean curvature is constant, is a sphere. Here we study the problem of symmetry of in a hyperplane in case satisfies: for any two points , on , with , the mean curvature at the first is not greater than that at the second. Symmetry need not always hold, but in this paper, we establish it under some additional condition for ....