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Miaomiao Zhu

Bio: Miaomiao Zhu is an academic researcher from Shanghai Jiao Tong University. The author has contributed to research in topics: Harmonic map & Riemann surface. The author has an hindex of 16, co-authored 63 publications receiving 666 citations. Previous affiliations of Miaomiao Zhu include University of Warwick & Max Planck Society.


Papers
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Journal ArticleDOI
Miaomiao Zhu1
TL;DR: In this paper, the generalized energy identity of harmonic maps from degenerating Riemann surfaces with uniformly bounded energy was studied and conditions that are both necessary and sufficient for the compactness in W 1,2 and C 0 modulo bubbles of sequences of such maps were given.
Abstract: We study harmonic maps from degenerating Riemann surfaces with uniformly bounded energy and show the so-called generalized energy identity We find conditions that are both necessary and sufficient for the compactness in W 1,2 and C 0 modulo bubbles of sequences of such maps

59 citations

Journal ArticleDOI
TL;DR: In this paper, the analytic regularity of Dirac-harmonic maps is studied in a geometric framework, including the appropriate boundary conditions, and it is shown that a weakly Diracharmonic map is smooth in the interior of the domain.
Abstract: Dirac-harmonic maps are a mathematical version (with commuting variables only) of the solutions of the field equations of the non-linear supersymmetric sigma model of quantum field theory. We explain this structure, including the appropriate boundary conditions, in a geometric framework. The main results of our paper are concerned with the analytic regularity theory of such Dirac-harmonic maps. We study Dirac-harmonic maps from a Riemannian surface to an arbitrary compact Riemannian manifold. We show that a weakly Diracharmonic map is smooth in the interior of the domain. We also prove regularity results for Dirac-harmonic maps at the boundary when they solve an appropriate boundary value problem which is the mathematical interpretation of the D-branes of superstring theory.

59 citations

Journal ArticleDOI
TL;DR: In this article , a green one-step electrospinning, eco-friendly curved-ribbon nanofiber membrane with multi-hierarchical structure was proposed for efficient, breathable and sustainable air filtration.

47 citations

Journal ArticleDOI
Miaomiao Zhu1
TL;DR: In this paper, a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface is shown to be smooth, and it is shown that the map is a weak Dirac map.
Abstract: We prove that a weakly Dirac-harmonic map from a Riemann spin surface to a compact hypersurface \({N \subset \mathbb{R}^{d+1}}\) is smooth.

41 citations

Journal ArticleDOI
TL;DR: In this paper, the authors established the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints, and proved full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces.
Abstract: We establish the regularity theory for certain critical elliptic systems with an anti-symmetric structure under inhomogeneous Neumann and Dirichlet boundary constraints. As applications, we prove full regularity and smooth estimates at the free boundary for weakly Dirac-harmonic maps from spin Riemann surfaces. Our methods also lead to the full interior \(\epsilon \)-regularity and smooth estimates for weakly Dirac-harmonic maps in all dimensions.

39 citations


Cited by
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Book ChapterDOI
01 Jan 2009

256 citations

Journal ArticleDOI
TL;DR: In this paper, a branched conformal immersion of compact Riemann surfaces with fixed genus and Willmore energy was studied, and it was shown that the map is unbranched under the assumption that π_k converges to π-Sigma in moduli space.
Abstract: We study sequences $f_k:\Sigma_k \to \R^n$ of conformally immersed, compact Riemann surfaces with fixed genus and Willmore energy ${\cal W}(f) \leq \Lambda$. Assume that $\Sigma_k$ converges to $\Sigma$ in moduli space, i.e. $\phi_k^\ast(\Sigma_k) \to \Sigma$ as complex structures for diffeomorphisms $\phi_k$. Then we construct a branched conformal immersion $f:\Sigma \to \R^n$ and M\"obius transformations $\sigma_k$, such that for a subsequence $\sigma_k \circ f_k \circ \phi_k \to f$ weakly in $W^{2,2}_{loc}$ away from finitely many points. For $\Lambda < 8\pi$ the map $f$ is unbranched. If the $\Sigma_k$ diverge in moduli space, then we show $\liminf_{k \to \infty} {\cal W}(f_k) \geq \min(8\pi,\omega^n_p)$. Our work generalizes results in \cite{K-S3} to arbitrary codimension.

97 citations

Book
01 Apr 1988
TL;DR: Papers by: S.A.H.H., C.T.M. Tucker, C.I.S.V.
Abstract: Papers by: S.H. Abed, O. Amici, A. Asada, V.V. Astrhancev, S. Bacso, J.K. Beem, A. Bejancu, K. Belteky, I.M. Benn, L. Biesk, T.Q. Binh, N. Blazic, N. Bokan, K. Buchner, B. Casciaro, A.V. Chakmazjan, I. Comic, A. Crumeyrolle, I. Dimitric, C.T.J. Dodson, P. Dragila, S. Dragomir, J.J. Duistermaat, P.E. Ehrlich, J. Eichhorn, M. Falcitelli, M. Ferraris, S. Formella, M. Francaviglia, S.I. Goldberg, A. Gray, T. Hangan, M. Husty, G. Ivan, A. Jakubowicz, S. Janeczko, Z. Jankovic, J. Klein, F.C. Klepp, I. Kolar, Z. Kovacs, L. Kozma, B. Lukacs, V.S. Malakhovsky, K.B. Marathe, S. Markvorsen, I. Mihai, J. Mikesh, R. Miron, E. Molnar, A.M. Naveira, J. Nikic, J. Novotny, V. Oliker, T. Otsuki, A.M. Pastore, Z. Perjes, J.F. Pommaret, M. Puta, H. Reckziegel, A.H. Rocamora, O. Roschel, H. Sachs, A. Sebestyen, U. Simon, H. Singh, G.A.J. Sparling, P. Stavre, S. Steiner, R. Sulanke, J. Szenthe, J. Szilasi, L. Tamassy, E. Teufel, F. Tricerri, R.W. Tucker, C. Udriste, I. Vaisman, L. Vanhecke, L. Verstraelen, V.A. Vujicic, P.G. Walczak, H. Yasuda, A. Zajtz, V. Zoller

92 citations