论文标题
将节点解决方案加倍到yamabe方程中的$ \ mathbb {r}^n $具有最大等级
Doubling nodal solutions to the Yamabe equation in $\mathbb{R}^n$ with maximal rank
论文作者
论文摘要
我们为Yamabe方程$$-ΔU= \ frac {n（n-2）} {4} | U |^{\ frac {\ frac {4} {n-2}} u \ mbox {in}解决方案具有最大等级，是奇数维度中的第一个示例。我们的构建类似于赤道球在$ s^3（1）$中的最小表面的构造中的翻倍。
We construct a new family of entire solutions to the Yamabe equation $$-Δu=\frac{n(n-2)}{4}|u|^{\frac{4}{n-2}}u \mbox{ in }\mathcal{D}^{1,2}(\mathbb{R}^n).$$ If $n=3$, our solutions have maximal rank, being the first example in odd dimension. Our construction has analogies with the doubling of the equatorial spheres in the construction of minimal surfaces in $S^3(1)$.
