Dimiter Vassilev, PhD

Publications

Count: 25

• Optimal decay for solutions of nonlocal semilinear equations with critical exponent in homogeneous groups (2024) — Nicola Garofalo, Annunziata Loiudice, Dimiter Vassilev — Proceedings of the Royal Society of Edinburgh: Section A Mathematics
  Abstract

  In this paper, we establish the sharp asymptotic decay of positive solutions of the Yamabe type equation $\mathcal {L}_s u=u^{\frac {Q+2s}{Q-2s}}$ in a homogeneous Lie group, where $\mathcal {L}_s$ represents a suitable pseudodifferential operator modelled on a class of nonlocal operators arising in conformal CR geometry.
• Overdetermined problems in groups of Heisenberg type: Conjectures and partial results (2024) — Nicola Garofalo, Dimiter Vassilev — Journal of Functional Analysis
• Solution of the qc Yamabe equation on a 3-Sasakian manifold and the quaternionic Heisenberg group (2023) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — Analysis & PDE
• On Sub-Riemannian and Riemannian Spaces Associated to a Lorentzian Manifold (2022) — Roman Sverdlov, Dimiter Vassilev — Trends in Mathematics
• Non-Umbilical Quaternionic Contact Hypersurfaces in Hyper-Kähler Manifolds (2019) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — International Mathematics Research Notices
  Abstract

  Abstract It is shown that any compact quaternionic contact (qc) hypersurfaces in a hyper-Kähler manifold which is not totally umbilical has an induced qc structure, locally qc homothetic to the standard 3-Sasakian sphere. In the non-compact case, it is proved that a seven-dimensional everywhere non-umbilical qc-hypersurface embedded in a hyper-Kähler manifold is qc-conformal to a qc-Einstein structure which is locally qc-equivalent to the 3-Sasakian sphere, the quaternionic Heisenberg group or the hyperboloid.
• Convexity of the entropy of positive solutions to the heat equation on quaternionic contact and CR manifolds (2017) — Dimiter Vassilev — Pacific Journal of Mathematics
• The Obata sphere theorems on a quaternionic contact manifold of dimension bigger than seven (2017) — Stefan Ivanov, Alexander Petkov, Dimiter Vassilev — Journal of Spectral Theory
  Abstract

  On a compact quaternionic contact (qc) manifold of dimension bigger than seven and satisfying a Lichnerowicz type lower bound estimate we show that if the rst positive eigenvalue of the sub-Laplacian takes the smallest possible value then, up to a homothety of the qc structure, the manifold is qc equivalent to the standard 3-Sasakian sphere. The same conclusion is shown to hold on a non-compact qc manifold which is complete with respect to the associated Riemannian metric assuming the existence of a function with traceless horizontal Hessian.
• Quaternionic Heisenberg Group and Heterotic String Solutions with Non-Constant Dilaton in Dimensions 7 and 5 (2015) — Marisa Fernández et al. — Communications in Mathematical Physics
• The Lichnerowicz and Obata first eigenvalue theorems and the Obata uniqueness result in the Yamabe problem on CR and quaternionic contact manifolds (2015) — Stefan Ivanov, Dimiter Vassilev — Nonlinear Analysis
• Non-Kaehler heterotic string solutions with non-zero fluxes and non-constant dilaton (2014) — Marisa Fernández et al. — Journal of High Energy Physics
• The sharp lower bound of the first eigenvalue of the sub-Laplacian on a quaternionic contact manifold in dimension seven (2013) — S. Ivanov, A. Petkov, D. Vassilev — Nonlinear Analysis: Theory, Methods & Applications
• An Obata type result for the first eigenvalue of the sub-Laplacian on a CR manifold with a divergence-free torsion (2012) — Stefan Ivanov, Dimiter Vassilev — Journal of Geometry
• The optimal constant in the L2 Folland-Stein inequality on the quaternionic Heisenberg group (2012) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
• $L^{p}$ estimates and asymptotic behavior for finite energy solutions of extremals to Hardy-Sobolev inequalities (2011) — Dimiter Vassilev — Transactions of the American Mathematical Society
• Extremals for the Sobolev Inequality and the Quaternionic Contact Yamabe Problem (2011) — Stefan P Ivanov, Dimiter N Vassilev — World Scientific, 2011
• Conformal quaternionic contact curvature and the local sphere theorem (2010) — Stefan Ivanov, Dimiter Vassilev — Journal de Mathématiques Pures et Appliquées
• Extremals for the Sobolev inequality on the seven-dimensional quaternionic Heisenberg group and the quaternionic contact Yamabe problem (2010) — Stefan Ivanov, Ivan Minchev, Dimiter Vassilev — Journal of the European Mathematical Society
  Abstract

  A complete solution to the quaternionic contact Yamabe problem on the seven dimensional sphere is given. Extremals for the Sobolev inequality on the seven dimensional Heisenberg group are explicitly described and the best constant in the L2 Folland–Stein embedding theorem is determined.
• Quaternionic contact manifolds with a closed fundamental 4-form (2010) — Stefan Ivanov, Dimiter Vassilev — Bulletin of the London Mathematical Society
• Strong Unique Continuation Properties of Generalized Baouendi–Grushin Operators (2007) — Nicola Garofalo, Dimiter Vassilev — Communications in Partial Differential Equations
• Existence of solutions and regularity near the characteristic boundary for sub-Laplacian equations on Carnot groups (2006) — Dimiter Vassilev — Pacific Journal of Mathematics
• A note on the stability of local zeta functions (2005) — Dimiter Vassilev — Proceedings of the American Mathematical Society
  Abstract

  We show the existence of an interval of stability under small perturbations of local zeta functions corresponding to non-trivial local solutions of an elliptic equation with Lipschitz coefficients. Résumé. Nous démontrons l’existence d’un intervalle de stabilité pour la fonction zêta associée à une équation uniformément elliptique du second ordre à coefficients lipschitziens.
• Overdetermined Boundary Value Problems, Quadrature Domains and Applications (2005) — Dmitry Khavinson, Alexander Yu. Solynin, Dimiter Vassilev — Computational Methods and Function Theory
• Strong Unique Continuation for Generalized Baouendi-Grushin Operators (2005) — Nicola Garofalo, Dimiter Vassilev — Proceedings of the 4th International ISAAC Congress
• Symmetry properties of positive entire solutions of Yamabe-type equations on groups of Heisenberg type (2001) — Nicola Garofalo, Dimiter Vassilev — Duke Mathematical Journal
• Regularity near the characteristic set in the non-linear Dirichlet problem and conformal geometry of sub-Laplacians on Carnot groups (2000) — Nicola Garofalo, Dimiter Vassilev — Mathematische Annalen