UNIVERSITY OF MIAMI
 

Pengzi Miao

Professor of Mathematics

Department of Mathematics
University of Miami
Coral Gables, FL 33146
Email: pengzim at math dot miami dot edu



EDUCATION

Ph.D. Mathematics. Stanford University 2003.

B.S. Mathematics. Peking University 1998.

RESEARCH INTERESTS

Differential Geometry, Mathematical Relativity


PUBLICATIONS

  1. P. Miao, Implications of some mass-capacity inequalities, J Geom Anal 34, 241 (2024), Open access https://doi.org/10.1007/s12220-024-01686-7

  2. P. Miao, Mass, capacitary functions, and the mass-to-capacity ratio, Peking Mathematical Journal, online first https://doi.org/10.1007/s42543-023-00071-7; access via Springer Nature SharedIt https://rdcu.be/dd6dq

  3. P. Miao, Interpreting mass via Riemannian polyhedra, Perspectives in Scalar Curvature, 739-759 (2023), edited by Mikhail L Gromov and H Blaine Lawson, Jr. Doi.org/10.1142/9789811273230_0020.

  4. P. Miao, Introduction to the Wang-Yau Quasi-local Energy. In: Cacciatori, S.L., Kamenshchik, A. (eds) Einstein Equations: Local Energy, Self-Force, and Fields in General Relativity, pp 3-23, (2023). Tutorials, Schools, and Workshops in the Mathematical Sciences. Birkhäuser, Cham. https://doi.org/10.1007/978-3-031-21845-3_1

  5. S. Hirsch, P. Miao and L.-F. Tam, Monotone quantities of p-harmonic functions and their applications, Pure and Applied Mathematics Quarterly, 20 (2): 599-644, 2024. [arXiv:2211.06939]

  6. P. Miao and A. Piubello, Estimates of the Bartnik mass, Beijing J. of Pure and Appl. Math., 1 (2): 489-513, 2024. [arXiv:2303.13633]

  7. H.C. Jang and P. Miao, Hyperbolic mass via horospheres, Commun. Contemp. Math., Vol. 25, No. 08, 2250023 (2023), https://doi.org/10.1142/S0219199722500237

  8. P. Miao and A. Piubello, Mass and Riemannian polyhedra, Adv. Math., 400 (2022), 108287. Doi.org/10.1016/j.aim.2022.108287. [arXiv:2101.02693]

  9. S. Lu and P. Miao, Rigidity of Riemannian Penrose inequality with corners and its implications, J. Funct. Anal., 281 (10): 109231-109241, 2021. [arXiv:2010.07963]

  10. P. Miao, Nonexistence of NNSC fill-ins with large mean curvature, Proc. Amer. Math. Soc., 149: 2705-2709, 2021. [arXiv:2009.04976]

  11. S. Hirsch, P. Miao and T.-Y. Tsang, Mass of asymptotically flat 3-manifolds with boundary, Comm. Anal. Geom., 31 (7): 1611-1653, 2023. [arXiv:2009.02959]

  12. P. Miao, Measuring mass via coordinate cubes, Commun. Math. Phys., 379: 773-783, 2020. [arXiv:1911.11757]

  13. C. Mantoulidis, P. Miao and L.-F. Tam, Capacity, quasi-local mass, and singular fill-ins, Journal für die reine und angewandte Mathematik, Crelle's Journal, 2020 (768): 55-92, 2020. [arXiv:1805.05493]

  14. P. Miao and N.Q. Xie, Bartnik mass via vacuum extensions, Internat. J. Math., 30 (13): 1940006, 11 pp, 2019, a special issue dedicated to the mathematical contribution of Luen-Fai Tam. [arXiv:1907.02039]

  15. P. Miao, On metrics that can be viewed as "localized Einstein metrics", Advanced Lectures in Mathematics 45: Tsinghua Lectures in Mathematics, pp. 345-359, edited by Lizhen Ji, Yat-Sun Poon and Shing-Tung Yau, Higher Education Press and International Press, Beijing-Boston, 2019.

  16. S. McCormick and P. Miao, On the evolution of the spacetime Bartnik mass, Pure and Applied Mathematics Quarterly, 15 (3): 897-920, 2019. [arXiv:1902.02284]

  17. S. Hirsch and P. Miao, A positive mass theorem for manifolds with boundary, Pacific J. Math., 306 (1): 185-201, 2020. [arXiv:1812.03961]

  18. P. Miao, Y. Wang and N.Q. Xie, On Hawking mass and Bartnik mass of CMC surfaces, Math. Res. Lett., 27 (3): 855-885, 2020. [arXiv:1809.04056]

  19. S. Lu and P. Miao, Variation and rigidity of quasi-local mass, Adv. Theor. Math. Phys., 23 (5): 1411-1426, 2019. [arXiv:1802.10070]

  20. C. Li, Z. Wang and P. Miao, Uniqueness of isometric immersions with the same mean curvature, J. Funct. Anal., 276 (9): 2831-2855, 2019. [arXiv:1802.04244]

  21. S. Lu and P. Miao, Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature, J. Differential Geom., 113: 519-566, 2019. [arXiv:1703.08164]

  22. L.-H. Huang, D. Martin and P. Miao, Static potentials and area minimizing hypersurfaces, Proc. Amer. Math. Soc., 146: 2647-2661, 2018. [arXiv:1706.03734]

  23. S. McCormick and P. Miao, On a Penrose-like inequality in dimensions less than eight, Int. Math. Res. Not. IMRN, Volume 2019, Issue 7, April 2019, 2069-2084. [arXiv:1701.04805]

  24. C. Mantoulidis and P. Miao, Mean curvature deficit and a quasi-local mass, Nonlinear Analysis in Geometry and Applied Mathematics, 99-107, Harvard University Center of Mathematical Sciences and Applications (CMSA) Series in Mathematics, Volume 1, Int. Press, Somerville, MA, 2017.

  25. A. J. Cabrera Pacheco, C. Cederbaum, S. McCormick and P. Miao, Asymptotically flat extensions of CMC Bartnik data, Class. Quantum Grav., 34: 105001 (15 pp), 2017. [arXiv:1612.05241]

  26. P. Miao and N.Q. Xie, On compact 3-manifolds with nonnegative scalar curvature with a CMC boundary component, Trans. Amer. Math. Soc., 370: 5887-5906, 2018. [arXiv:1610.07513]

  27. C. Mantoulidis and P. Miao, Total mean curvature, scalar curvature, and a variational analog of Brown-York mass, Commun. Math. Phys., 352 (2): 703-718, 2017. [arXiv:1604.00927]

  28. P. Miao, L.-F. Tam and N.Q. Xie, Quasi-local mass integrals and the total mass, J Geom Anal, 27: 1323-1354, 2017. [arXiv:1510.07756]

  29. P. Miao and L.-F. Tam, Some functionals on compact manifolds with boundary, Math. Z., 286 (3-4): 1525-1537, 2017. [arXiv:1602.06616]

  30. A. J. Cabrera Pacheco and P. Miao, Higher dimensional black hole initial data with prescribed boundary metric, Math. Res. Lett., 25 (3): 937-956, 2018. [arXiv:1505.01800]

  31. P. Miao, Quasi-local mass via isometric embeddings: a review from a geometric perspective, invited contribution as a Topical Review, Class. Quantum Grav., 32: 233001 (18pp), 2015.

  32. K.-K. Kwong and P. Miao, A functional inequality on the boundary of static manifolds, Asian J. Math., 21 (4): 687-695, 2017. [arXiv:1602.00194]

  33. A. J. Cabrera Pacheco and P. Miao, Isometric embeddings of 2-spheres into Schwarzschild manifolds, Manuscripta Math., 149: 459-469, 2016.

  34. P. Miao and X. Wang, Boundary effect of Ricci curvature, J. Differential Geom., 103 (1): 59-82, 2016. [arXiv:1408.2711]

  35. G. Galloway and P. Miao, Variational and rigidity properties of static potentials, Comm. Anal. Geom., 25 (1): 163-183, 2017. [arXiv:1412.1062]

  36. P. Miao and L.-F. Tam, Evaluation of the ADM mass and center of mass via the Ricci tensor, Proc. Amer. Math. Soc., 144: 753-761, 2016. [arXiv:1408.3893]

  37. G. Galloway, P. Miao and R. Schoen, Initial Data and the Einstein Constraint Equations, General Relativity and Gravitation: A Centennial Perspective, Cambridge University Press, 2015.

  38. P. Miao and L.-F. Tam, Static potentials on asymptotically flat manifolds, Ann. Henri Poincaré., 16 (10): 2239-2264, 2015. [arXiv:1403.4001]

  39. K.-K. Kwong and P. Miao, Monotone quantities involving a weighted σk integral along inverse curvature flows, Commun. Contemp. Math., 17 (5): 1550014 (10 pages), 2015. [arXiv:1402.0843]

  40. J. Jauregui, P. Miao and L.-F. Tam, Extensions and fill-ins with nonnegative scalar curvature, Class. Quantum Grav., 30: 195007-195018, 2013. [arXiv:1304.0721]

    This article has been selected for inclusion in IOPselect.

  41. P. Miao and L.-F. Tam, On second variation of Wang-Yau quasi-local energy, Ann. Henri Poincaré., 15 (7): 1367-1402, 2014. [arXiv:1301.4656]

  42. K.-K. Kwong and P. Miao, A new monotone quantity along the inverse mean curvature flow in R^n, Pacific J. Math., 267 (2): 417-422, 2014. [arXiv:1212.1906]

  43. J. Corvino, M. Eichmair and P. Miao, Deformation of scalar curvature and volume, Math. Ann., 357: 551-584, 2013. [arXiv:1211.6168]

  44. G. Cox, P. Miao and L.-F. Tam, Remarks on a scalar curvature rigidity theorem of Brendle and Marques, Asian J. Math., 17 (3): 457-470, 2013. [arXiv:1109.3942]

  45. P. Miao and L.-F. Tam, Scalar curvature rigidity with a volume constraint, Comm. Anal. Geom., 20 (1): 1-30, 2012. [arXiv:1109.2960]

  46. P. Miao, A survey of research on boundary behavior of compact manifolds via the positive mass theorem, Surveys in Geometric Analysis and Relativity, Adv. Lect. Math. (ALM), 20: 395-411, Int. Press, Somerville, MA, 2011.

  47. P. Miao, L.-F. Tam and N.Q. Xie, Critical points of Wang-Yau quasi-local energy, Ann. Henri Poincaré., 12 (5): 987-1017, 2011. [arXiv:1003.5048]

  48. M. Eichmair, P. Miao and X. Wang, Extension of a theorem of Shi and Tam, Calc. Var. Partial Differential Equations., 43 (1-2): 45-56, 2012. [arXiv:0911.0377]

  49. P. Miao, L.-F. Tam and N.Q. Xie, Some estimates of Wang-Yau quasilocal energy, Class. Quantum Grav., 26: 245017-245029, 2009. [arXiv:0909.0880]

  50. P. Miao, Y.G. Shi and L.-F. Tam, On geometric problems related to Brown-York and Liu-Yau quasilocal mass, Commun. Math. Phys., 298 (2): 437-459, 2010. [arXiv:0906.5451]

  51. P. Miao, On a localized Riemannian Penrose inequality, Commun. Math. Phys., 292: 271-284, 2009. [arXiv:0901.2697]

  52. P. Miao and L.-F. Tam, Einstein and conformally flat critical metrics of the volume functional, Trans. Amer. Math. Soc., 363 (6): 2907-2937, 2011. [arXiv:0901.0422]

  53. P. Miao and L.-F. Tam, On the volume functional of compact manifolds with boundary with constant scalar curvature, Cal. Var. Partial Differential Equations, 36 (2): 141-171, 2009. [arXiv:0807.2693]

  54. H. Bray and P. Miao, On the capacity of surfaces in manifolds with nonnegative scalar curvature, Invent. Math., 172 (3): 459-475, 2008. [arXiv:0707.3337]

  55. P. Miao, Some recent developments of the Bartnik mass, Proceedings of the Fourth International Congress of Chinese Mathematicians, Volume III: 331--340, High Educational Press, Beijing, 2007. [Download this paper here]

  56. P. Miao, A note on existence and non-existence of minimal surfaces in some asymptotically flat 3-manifolds, Math. Res. Lett., 14 (3): 395-402, 2007. [arXiv:math/0601480]

  57. P. Miao, A remark on boundary effects in static vacuum initial data sets, Class. Quantum Grav., 22: L53-L59, 2005.

  58. P. Miao, Proof of the rigidity of hyperbolic spaces using quasilocal mass type theorems, J. Hyperbolic Differ. Equ., 2 (2), 2005.

  59. V. Bonini, P. Miao and J. Qing, Ricci curvature rigidity for weakly asymptotically hyperbolic manifolds, Comm. Anal. Geom., 14 (3): 603 -- 612, 2006.

  60. P. Miao, Variational effect of boundary mean curvature on ADM mass in general relativity, Mathematical Physics Research on the Leading Edge, 145-171, Nova Sci. Publ., Hauppauge, New York, 2004.

  61. P. Miao, Asymptotically flat and scalar flat metrics on R^3 admitting a horizon, Proc. Amer. Math. Soc., 132: 217-222, 2004.

  62. P. Miao, Minimizing energy among homotopic maps, Int. J. Math. and Math. Sci., 30: 1599-1611, 2004.

  63. P. Miao, On existence of static metric extensions in general relativity, Commun. Math. Phys., 241 (1): 27-46, 2003.

  64. P. Miao, Positive mass theorem on manifolds admitting corners along a hypersurface, Adv. Theor. Math. Phys., 6 (6): 1163--1182, 2002.


Last Updated: August, 2024.



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