Ali Hyder

Postdoctoral Fellow  

Department of Mathematics
Johns Hopkins University

Krieger Hall
Room  221
Baltimore, MD, 21218

E-mail:  ahyder4@jhu.edu

Research Interests

• Nonlinear partial differential equations
• Conformal geometry
• Moser-Trudinger inequalities
• Nonlocal equations
• Harmonic maps
• Partial regularity

Publications

1. Local and nonlocal problems regarding the Q-curvature and the Adams-Moser-Trudinger inequalities
   Doctoral Dissertation (2017),  (Download)
   
2. Conformal metrics on R^2m with constant Q-curvature, prescribed volume and asymptotic behavior
   (With L. Martinazzi) Discrete Contin. Dynam. Systems, A. 35 (2015),  no. 1, 283-299. (Journal/arXiv)
3. Existence of entire solutions to a fractional Liouville equation in R^n
   Rend. Lincei. Mat. Appl. 27 (2016), 1-14. (Journal/arXiv)
4. Moser functions and fractional Moser-Trudinger type inequalities
   Nonlinear Analysis. 146 (2016), 185-210. (Journal/arXiv)
5. Conformally Euclidean metrics on R^n with arbitrary total Q-curvature
   Analysis & PDE. 10 (2017), no. 3, 635-652. (Journal/arXiv)
6. Large blow-up sets for the prescribed Q-curvature equation in the Euclidean space
   (With S. Iula and  L. Martinazzi) Commun. Contemp. Math (2018), (Journal/arXiv)
7. Structure of conformal metrics on R^n with constant Q-curvature
   Differential and Integral Equations 32 (2019), no. 7-8, 423-454. (Journal/arXiv)
8. The non-local mean-field equation on an interval
   (With A. Delatorre, L. Martinazzi and Y. Sire) Commun. Contemp. Math (2019) (Journal/arXiv)
9. Higher order conformally invariant equations in R^3 with prescribed volume
   (With J. Wei) Comm. Pure Appl. Anal. 18(5): (2019) 2757-2764. (Jounal/arXiv)
10. Local and nonlocal singular Liouville equations in Euclidean spaces,
    (With G. Mancini and L. Martinazzi) Int. Math. Res. Not. (IMRN) (2019). (Journal/arXiv)
11. Non-radial solutions to a bi-harmonic negative exponent problem
    (With J. Wei)  Calc. Var. PDE. (2019), Paper No. 198, 11pp.  (Journal/arXiv)  
12. On SU(3) Toda system with multiple singular sources
    (With C.-S. Lin and  J. Wei) Pacific J. Mathematics, 305 (2020), 645-666.  (Journal/arXiv)
13. On the general Toda system with multiple singular points
    (With J. Wei and W. Yang)  Calc. Var. PDE 59 (2020) Paper No. 136. (Journal/arXiv)
14. Concentration phenomena to a higher order Liouville equation
    Calc. Var. PDE 59  (2020) Paper No. 126. (Journal/arXiv)
15. Gluing metrics with prescribed Q-curvature and different asymptotic behaviour in high dimension
    (With L. Martinazzi)  To appear in Ann. Sc. Norm. Super. Pisa Cl. Sci. (2021). (Journal/arXiv)
16. Removability of singularities and superharmonicity for some fractional Laplacian equations
    (With W. Ao, M. D. M. Gonzalez and J. Wei)  To appear in Indiana Univ. Math. J.  (Journal/arXiv)
17. Classification of stable solutions to a non-local Gelfand-Liouville equation
    (With W. Yang) To appear in Int. Math. Res. Not. (IMRN). (arXiv)
18. Singular solutions for the constant Q-curvature problem
    (With Y. Sire) To appear in J. Functional Analysis. (arXiv)
    
19. Concentration phenomena for the fractional Q-curvature equation in dimension 3
    (With A. Delatorre, M. D. M. Gonzalez and L. Martinazzi) Preprint, (2018). (arXiv)
20. Singular Yamabe metrics by equivariant reduction
    (With A. Pistoia and Y. Sire)  Preprint (2020). (arXiv)
    

My research profile in MathScinet ResearchGate ORCID