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- W1822295730 abstract "We prove the removal singularity results for maps with bounded energy from the unit disk $B$ of $R^2$ centered at the origin to a closed Riemannian manifold whose tension field is unbounded in $L^2(B)$ but satisfies the following condition: {eqnarray*} (int_{B_tsetminus B_{frac{t}{2}}}|tau(u)|^2)^1/2leq C_1(frac{1}{t})^a, {eqnarray*} for some $0<a<1$ and for any $0<t<1$, where $C_1$ is a constant independent of $t$. We will also prove that if a sequence ${u_n}$ has uniformly bounded energy and satisfies {eqnarray*} (int_{B_tsetminus B_{frac{t}{2}}}|tau(u_n)|^2)^1/2leq C_2(frac{1}{t})^a, {eqnarray*} for some $0<a<1$ and for any $0<t<1$, where $C_2$ is a constant independent of $n$ and $t$, then the energy identity holds for this sequence and there will be no neck formation during the blow up process." @default.
- W1822295730 created "2016-06-24" @default.
- W1822295730 creator A5055358055 @default.
- W1822295730 date "2011-10-21" @default.
- W1822295730 modified "2023-09-27" @default.
- W1822295730 title "On maps from a Riemann surface with tension field unbounded in $L^2$" @default.
- W1822295730 hasPublicationYear "2011" @default.
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