Publications:

(Publications before 1997) | (Non-research articles) | (Full publication list) | (Other papers)

Thesis
  1. Ph.  D Thesis, The Courant Institute, NYU, 1997
Publications
  1. A note on special Kahler manifolds, Math. Ann., vol 313, 1999, pp 711-713
  2. On the geometry of classifying spaces and horizontal Slices, Amer. J. Math, vol 121, 1999, pp 177-198
  3. On the Futaki invariants of complete intersections, Duke J. Math, vol 100(2), 1999, pp 359-372
  4. On the lower order terms of the asymptotic expansion of Tian-Yau-Zelditch, Amer. J. Math, vol 122(2), 2000, pp 235-273
  5. On the Hodge metric of the universal deformation space of Calabi-Yau threefolds, J. Geom. Anal., vol 11(1), 2001, pp 103-118
  6. On the curvature tensor of the Hodge metric of moduli space of polarized Calabi-Yau threefolds, J. Geom. Anal., vol 11(4), 2001, pp 635-647
  7. On the lower bound estimates of sections of the canonical bundle over a Riemanns surface, Inter. J. Math, vol 12(8), 2001, pp 235-273
  8. (with X. Sun) Weil-Petersson geometry on moduli space of polarized Calabi-Yau manifolds, J. Inst. Math. Jussieu, vol 3(2), 2004, pp 185-229
  9. (with G. Tian) The log term of Szego kernel, Duke J. Math, vol 125(2), 2004, pp 351-387
  10. K energy and K stability on hypersurfaces, Comm. Anal. Geom., vol 12(3), 2004, pp 599-628
  11. (with H. Fang) Generalized Hodge metrics and BCOV torsion on Calabi-Yau moduli, J. Reine Angew. Math., vol 588, 2005, 49-69
  12. (with X. Sun) On the Weil-Petersson volume of the moduli space of Calabi-Yau manifolds, Comm. Math. Phys., vol 261, 2006, 297-322
  13. (with C. Lin) On the discrete spectrum of generalized quantum tubes, Comm. PDE, vol 31, 2006, pp 1529-1546
  14. (with C. Lin) Existence of bound stated for layers built over hypersurfaces in Euclidean space, J. Funct. Anal., vol 244(1), 2007, pp 1-25
  15. (with C. Lin) Quantum layers over surfaces ruled outside a compact set, J. Math. Phys., vol 48, 2007, 053522
  16. (with T. Choi) On the DDVV Conjecture and the comass in Calibrated geometry (I), Math Z., vol 260, 2008, pp 409-429
  17. (with H. Fang and K. Yoshikawa) Asymptotic behavior of the BCOV torsion of Calabi-Yau moduli, J. Diff. Geom., vol 80, 2008, pp 175-259
  18. (with J. Ling) Bounds of eigenvalues on Riemannian manifolds, Trends in partial differential equations, 241–264, Adv. Lect. Math. (ALM), 10, Int. Press, Somerville, MA, 2010
  19. (with D. Zhou) On the essential spectrum of complete non-compact manifolds, J. Funct. Anal. vol 260, 2011, pp 3283–3298
  20. Normal scalar curvature conjecture and its applications, J. Funct. Anal, vol 261, 2011, pp 1284-1308
  21. (with P. Baldi) Complex-valued autoencoders, Neural Networks, vol 33, 2012, pp 136-147
  22. (with J. Rowlett) On the discrete spectrum of quantum layers, J. Math Phys., vol 53 (7), 2012, 073519
  23. (with J. Rowlett) Eigenvalues of collapsing domains and drift Laplacians, Math Res. Lett., vol 19(3), 2012, pp 627-648
  24. (with J. Rowlett) The fundamental gap of simplices, Comm. Math. Phys., vol 319, 2013, pp 111-145
  25. (with M. Douglas) Gauss-Bonnet-Chern theorem on moduli space, Math. Ann., vol 357, 2013, pp 469-511
  26. (with N. Charalambous) On the spectrum of the Laplacian, Math. Ann., vol 359, 2014, 211-238
  27. (with R. Seyyedali) Extremal metrics on ruled manifolds, Adv. Math., vol 258, 2014, 127-153
  28. (with D. Krejcirik) Location of the essential spectrum in curved quantum layers, J. Math Phys., vol 55, 2014, 083520
  29. (with N. Charalambous) Heat kernel estimates and the essential spectrum on weighted manifolds, J. Geom. Anal., vol 25, 2015, pp 536-563
  30. (with Bernard Shiffman) Asymptotic expansion of the off-diagonal Bergman kernel on compact Kahler manifolds, J. Geom. Anal., vol 25, 2015, pp 536-563
  31. (with C-J. Liu) Uniform asymptotic expansion on Riemann surfaces, Contemporary Mathematics, Analysis, Complex Geometry, and Mathematical Physics: a Conference in Honor of Duong H. Phong, vol 644, 2015, pp 159-173
  32. (with Steven Zelditch) Szego kernels and Poincare series, J. Anal. Math., vol 130, 2016, 167-184
  33. (with David Wenzel) The normal Ricci curvature inequality, Recent advances in the geometry of submanifolds---dedicated to the memory of Franki Dillen (1963--2013), Contemporary Mathematicsvol 674, 2016, 99-110
  34. (Joint with J. Rowlett), One can hear the corners of a drum, Bull. Lond. Math. Soc., vol 48, 2016, pp 85-93
  35. (with C-J. Liu) Abstract Bergman kernel expansion and its applications, Trans. Amer. Math. Soc., vol 368(2), 2016, pp 1467-1495
  36. (with D. Wenzel) Commutator Estimates Comprising the Frobenius Norm -- Looking Back and Forth, Operator Theory, vol 259, 2017, 533-559
  37. (with P. Baldi and P. Sadowski) Learning in the Machine: the Symmetries of the Deep Learning Channel, Neural Networks, vol 95, 2017, 110-133
  38. (with H. Hezari and J. Rowlett) The Neumann isospectral problem for trapezoids, Ann. Henri Poincare, vol 18(12) 2017, 3759–3792.
  39. (with Y. Wang) On locally conformally flat manifolds with finite total $Q$-curvature, Calc. Var. Partial Differential Equations , vol 56(4), 2017, Art. 98, 24 pp.
  40. (with P. Baldi and P. Sadowski) Learning in the machine: random backpropagation and the deep learning channel, Artificial Intelligence, vol 260, 2018, 1–35.