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• W3097165302 abstract "In this paper we show that locally there exists a Willmore deformation between minimal surfaces in $S^{n+2}$ and minimal surfaces in $H^{n+2}$, i.e., there exists a smooth family of Willmore surfaces ${y_t,tin[0,1]}$ such that $(y_t)|_{t=0}$ is conformally equivalent to a minimal surface in $S^{n+2}$ and $(y_t)|_{t=1}$ is conformally equivalent to a minimal surface in $H^{n+2}$. For some cases the deformations are global. Consider the Willmore deformations of the Veronese two-sphere and its generalizations in $S^4$, for any positive number $W_0inmathbb R^+$, we construct complete minimal surfaces in $H^4$ with Willmore energy being equal to $W_0$. An example of complete minimal Mobius strip in $H^4$ with Willmore energy $frac{6sqrt{5}pi}{5}approx10.733pi$ is also presented. We also show that all isotropic minimal surfaces in $S^4$ admit Jacobi fields different from Killing fields, i.e., they are not isolated." @default.
• W3097165302 created "2020-11-09" @default.
• W3097165302 creator A5037696275 @default.
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• W3097165302 date "2020-11-02" @default.
• W3097165302 modified "2023-09-23" @default.
• W3097165302 title "Willmore deformations between minimal surfaces in $H^{n+2}$ and $S^{n+2}$" @default.
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