**Professor of Mathematics**

University of Miami

Coral Gables, FL 33146

Email: pengzim at math dot miami dot edu

Ph.D. Mathematics. Stanford University 2003. Advisor: Richard M. Schoen.

B.S. Mathematics. Peking University 1998.

I am primarily interested in differential geometry and general relativity.

My research has been funded by

- P. Miao and N.Q. Xie,
*Bartnik mass via vacuum extensions*, International Journal of Mathematics, a special issue dedicated to the mathematical contribution of Luen-Fai Tam, https://doi.org/10.1142/S0129167X19400068. [arXiv:1907.02039] - 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. - S. McCormick and P. Miao,
*On the evolution of the spacetime Bartnik mass*, Pure and Applied Mathematics Quarterly., to appear. [arXiv:1902.02284] - C. Mantoulidis, P. Miao and L.-F. Tam,
*Capacity, quasi-local mass, singular fill-ins*, Journal für die reine und angewandte Mathematik, Crelle's Journal, to appear. [arXiv:1805.05493] - P. Miao and S. Hirsch,
*A positive mass theorem for manifolds with boundary*, submitted. [arXiv:1812.03961] - P. Miao, Y. Wang and N.Q. Xie,
*On Hawking mass and Bartnik mass of CMC surfaces*, Math. Res. Lett., to appear. [arXiv:1809.04056] - S. Lu and P. Miao,
*Variation and rigidity of quasi-local mass*, Adv. Theor. Math. Phys., to appear. [arXiv:1802.10070] - 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] - S. Lu and P. Miao,
*Minimal hypersurfaces and boundary behavior of compact manifolds with nonnegative scalar curvature*, J. Differential Geom., to appear., [arXiv:1703.08164] - 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] - 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] - 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. - 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] - 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] - 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] - 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] - P. Miao and L.-F. Tam,
*Some functionals on compact manifolds with boundary*, Math. Z.,**286**(3-4): 1525-1537, 2017. [arXiv:1602.06616] - 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] - 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. - 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] - A. J. Cabrera Pacheco and P. Miao,
*Isometric embeddings of 2-spheres into Schwarzschild manifolds*, Manuscripta Math.,**149**: 459-469, 2016. - P. Miao and X. Wang,
*Boundary effect of Ricci curvature*, J. Differential Geom.,**103**(1): 59-82, 2016. [arXiv:1408.2711] - G. Galloway and P. Miao,
*Variational and rigidity properties of static potentials*, Comm. Anal. Geom.,**25**(1): 163-183, 2017. [arXiv:1412.1062] - 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] - 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. - P. Miao and L.-F. Tam,
*Static potentials on asymptotically flat manifolds*, Ann. Henri Poincaré.,**16**(10): 2239-2264, 2015. [arXiv:1403.4001] - K.-K. Kwong and P. Miao,
*Monotone quantities involving a weighted σ*, Commun. Contemp. Math.,_{k}integral along inverse curvature flows**17**(5): 1550014 (10 pages), 2015. [arXiv:1402.0843] - 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.

- 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] - 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] - J. Corvino, M. Eichmair and P. Miao,
*Deformation of scalar curvature and volume*, Math. Ann.,**357**: 551-584, 2013. [arXiv:1211.6168] - 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] - P. Miao and L.-F. Tam,
*Scalar curvature rigidity with a volume constraint*, Comm. Anal. Geom.,**20**(1): 1-30, 2012. [arXiv:1109.2960] - 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. - 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] - 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] - 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] - 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] - P. Miao,
*On a localized Riemannian Penrose inequality*, Commun. Math. Phys.,**292**: 271-284, 2009. [arXiv:0901.2697] - 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] - 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] - 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] - 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] - 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] - P. Miao,
*A remark on boundary effects in static vacuum initial data sets*, Class. Quantum Grav.,**22**: L53-L59, 2005. - P. Miao,
*Proof of the rigidity of hyperbolic spaces using quasilocal mass type theorems*, J. Hyperbolic Differ. Equ.,**2**(2), 2005. - V. Bonini, P. Miao and J. Qing,
*Ricci curvature rigidity for weakly asymptotically hyperbolic manifolds*, Comm. Anal. Geom.,**14**(3): 603 -- 612, 2006. - 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. - P. Miao,
*Asymptotically flat and scalar flat metrics on R^3 admitting a horizon*, Proc. Amer. Math. Soc.,**132**: 217-222, 2004. - P. Miao,
*Minimizing energy among homotopic maps*, Int. J. Math. and Math. Sci.,**30**: 1599-1611, 2004. - P. Miao,
*On existence of static metric extensions in general relativity*, Commun. Math. Phys.,**241**(1): 27-46, 2003. - P. Miao,
*Positive mass theorem on manifolds admitting corners along a hypersurface*, Adv. Theor. Math. Phys.,**6**(6): 1163--1182, 2002.

* Last Updated: September 2019. *