Solitons of mean curvature flow in certain warped products: nonexistence, rigidity, and Moser-Bernstein type results

Year 2025, Volume: 8 Issue: 2, 117 - 134, 15.06.2025

Márcio Batista , Henrique De Lima Wallace Gomes

https://doi.org/10.33205/cma.1597851

Abstract

We apply suitable maximum principles to obtain nonexistence and rigidity results for complete mean curvature flow solitons in certain warped product spaces. We also provide applications to self-shrinkers in Euclidean space, as well as to mean curvature flow solitons in real projective, pseudo-hyperbolic, Schwarzschild, and Reissner-Nordstr\"{o}m spaces. Furthermore, we establish new Moser-Bernstein type results for entire graphs constructed over the fiber of the ambient space that are mean curvature flow solitons.

Keywords

Warped products, Euclidean space, real projective space, pseudo-hyperbolic spaces, Schwarzschild and Reissner-Nordström spaces, mean curvature flow solitons, self-shrinkers

Belirli Çarpık Ürünlerde Ortalama Eğrilik Akışının Solitonları: Yokluk, Sertlik ve Moser-Bernstein Tipi Sonuçlar

Abstract

Uygun maksimum ilkeleri uygulayarak, belirli çarpık ürün uzaylarında tam ortalama eğrilik akışı solitonları için yokluk ve sertlik sonuçları elde ediyoruz. Ayrıca, Öklid uzayındaki kendi kendine küçülen yüzeylere ve gerçek projektif, pseudo-hiperbolik, Schwarzschild ve Reissner-Nordström uzaylarındaki ortalama eğrilik akışı solitonlarına uygulamalar sağlıyoruz. Bunun yanı sıra, ortam uzayının lifleri üzerinde inşa edilen ve ortalama eğrilik akışı solitonları olan tüm grafikler için yeni Moser-Bernstein tipi sonuçlar ortaya koyuyoruz.

Keywords

Mean curvature flow;, Euclidean space;, Soliton;

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