We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in R^(n+1). If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2≤n≤1...We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in R^(n+1). If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2≤n≤10, it is unstable; while for n≥11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n≥2, it is unstable.展开更多
基金supported by National Natural Science Foundation of China (Grant Nos. 11271214 and 11671224)Ben Andrews’ ARC Laureate Fellowship (Grant No. FL150100126)
文摘We study the stability of unduloids with free boundary in the domain B between two parallel hyperplanes in R^(n+1). If the unduloid has one half of period in B and is sufficiently close to a cylinder, then for 2≤n≤10, it is unstable; while for n≥11, it is stable. If the unduloid has two or more halves of period in B and is sufficiently close to a cylinder, then for all n≥2, it is unstable.
