Authors	Title	Journal
Marcin Sroka	Sharp uniform bound for the quaternionic Monge-Ampere equation on hyperhermitian manifolds	Calc. Var., 63, article number 102, 2024
Abstract We provide the sharp C0 estimate for the quaternionic Monge-Ampere equation on any hyperhermitian manifold. This improves previously known results concerning this estimate in two directions. Namely, it turns out that the estimate depends only on Lp norm of the right hand side for any p > 2 (as suggested by the local case studied in [Sr20a]). Moreover, the estimate still holds true for any hyperhermitian initial metric - regardless of it being HKT as in the original conjecture of Alesker-Verbitsky [AV10] - as speculated by the author in [Sr21]. For completeness, we actually provide a sharp uniform estimate for many quaternionic PDEs, in particular those given by the operator dominating the quaternionic Monge-Ampere operator.
Sławomir Dinew, Marcin Sroka	On the Alesker-Verbitsky conjecture on hyperKahler manifolds	Geom. Funct. Anal. (GAFA), 33, 875-911, 2023
Abstract We solve the quaternionic Monge-Ampere equation on hyperKahler manifolds. In this way we prove the ansatz for the conjecture raised by Alesker and Verbitsky claiming that this equation should be solvable on any hyperKahler with torsion manifold, at least when the canonical bundle is trivial holomorphically. The novelty in our approach is that we do not assume any flatness of the underlying hypercomplex structure which was the case in all the approaches for the higher order a priori estimates so far. The resulting Calabi-Yau type theorem for HKT metrics is discussed.
Marcin Sroka	The C0 estimate for the quaternionic Calabi conjecture	Adv. Math, 70, Article 107237, 2020
Abstract We prove the C0 estimate for the quaternionic Monge-Ampere equation on compact hyperKahler with torsion manifolds. Our goal is to provide a simpler proof than the one presented in [3].
Sławomir Kołodziej, Marcin Sroka	Regularity of solutions to the quaternionic Monge-Ampere equation	J. Geom. Anal., 30(3), 2852-2864, 2020
Abstract The regularity of solutions to the Dirichlet problem for the quaternionic Monge-Ampere equation is discussed. We prove that the solution to the Dirichlet problem is Holder continuous under some conditions on the boundary values and the quaternionic Monge-Ampere density from Lp(Ω) for p > 2. As a step towards the proof, we provide a refined version of stability for the weak solutions to this equation.
Marcin Sroka	Weak solutions to the quaternionic Monge-Ampere equation	Anal. PDE, 13(6), 1755-1776, 2020
Abstract We solve the Dirichlet problem for the quaternionic Monge-Ampere equation with a continuous boundary data and the right-hand side in Lp for p > 2. This is the optimal bound on p. We prove also that the local integrability exponent of quaternionic plurisubharmonic functions is 2, which turns out to be less than an integrability exponent of the fundamental solution.
Marcin Sroka	Monge-Ampere equation in hypercomplex geometry	PhD thesis
Abstract We provide number of results concerning the quaternionic Monge-Ampere equation. This is the type of partial differential equation which appears in the presence of the hyperhermitian structure. For domains in the affine space we solve the Dirichlet problem for a continuous boundary data and the right hand side in Lp for p > 2. This generalizes many previous results on that problem. We show that this assumption on p is optimal. On compact hyperKahler with torsion manifolds we present the proof of the uniform a priori estimate for this equation.
Marcin Sroka	Existence of complex structures on decomposable Lie algebras	Univ. Iagel. Acta Math., 57, 25-58, 2020
Abstract We provide the classification of the six-dimensional decomposable Lie algebras, with the dimension of the biggest indecomposable summand less than five, admitting complex structures.
Andrzej Czarnecki, Marcin Sroka	Six-dimensional product Lie algebras admitting integrable complex structures	J. Pure Appl. Algebra, 222, 1111-1125, 2018
Abstract We classify the 6-dimensional Lie algebras of the form g ✕ g that admit an integrable complex structure. We also endow a Lie algebra of the kind o(n) ✕ o(n) (n ≥ 2) with such a complex structure. The motivation comes from geometric structures a' la Sasaki on manifolds.