Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2024, Cilt: 17 Sayı: 1, 245 - 251, 23.04.2024

Shoo Seto

https://doi.org/10.36890/iejg.1436665

Öz

Kaynakça

  • [1] Aubry, E.: Finiteness of π1 and geometric inequalities in almost positive Ricci curvature. Ann. Sci. École Norm. Sup. 40 (4), 675–695 (2007).
  • [2] Bakry D., Émery, M.: Diffusions hypercontractives. Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 177–206 (1985).
  • [3] Gallot, S.: Isoperimetric inequalities based on integral norms of Ricci curvature. Astérisque 157–158, Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987), 191–216 (1988).
  • [4] Li, F., Wu, J.-Y., Zheng, Y.: Myers’ type theorem for integral Bakry-Émery Ricci tensor bounds. Results Math. 76 (1), Paper No. 32, (2021).
  • [5] Petersen, P., Wei, G., Relative volume comparison with integral curvature bounds. Geom. Funct. Anal. 7 (6), 1031–1045 (1997).
  • [6] Ramos Olivé, X., Seto, S. Gradient Estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition, Preprint (2024).
  • [7] Seto, S., Wei, G. First eigenvalue of the p-Laplacian under integral curvature condition. Nonlinear Anal. 163, 60–70 (2017).
  • [8] Tolksdorf, P.: Regularity for a more general class of quasilinear elliptic equation. J. Differential Equations 51 (1), 126–150 (1984).
  • [9] Wang, Y.-Z., Li, H.-Q.Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces. Differential Geom. Appl. 45, 23–42 (2016).
  • [10] Wang, L., Wei, G. Local Sobolev constant estimate for integral Bakry-Émery Ricci curvature. Pacific J. Math. 300 (1), 233–256 (2019).
  • [11] Wei, G., Wylie, W. Comparison geometry for the Bakry-Émery Rici tensor. J. Differential Geom. 83 (2), 377–405 (2009).
  • [12] Wu, J.-Y. Comparison geometry for integral Bakry-Émery Ricci tensor bounds. J. Geom. Anal. 29 (1), 828–867 (2019).

Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds

Yıl 2024, Cilt: 17 Sayı: 1, 245 - 251, 23.04.2024

Shoo Seto

https://doi.org/10.36890/iejg.1436665

Öz

In this short note, we prove a quantitative lower bound in terms of the dimension and curvature,
known as a Lichnerowicz-type estimate, for the first eigenvalue of the p-Laplacian on Riemannian
manifolds with a bound on the integral norm of the Bakry-Émery curvature.

Anahtar Kelimeler

$p$-Laplacian Bakry-Emery curvature integral curvature

Teşekkür

Thank you for your consideration

Kaynakça

  • [1] Aubry, E.: Finiteness of π1 and geometric inequalities in almost positive Ricci curvature. Ann. Sci. École Norm. Sup. 40 (4), 675–695 (2007).
  • [2] Bakry D., Émery, M.: Diffusions hypercontractives. Séminaire de probabilités, XIX, 1983/84, Lecture Notes in Math., vol. 1123, Springer, Berlin, 177–206 (1985).
  • [3] Gallot, S.: Isoperimetric inequalities based on integral norms of Ricci curvature. Astérisque 157–158, Colloque Paul Lévy sur les Processus Stochastiques (Palaiseau, 1987), 191–216 (1988).
  • [4] Li, F., Wu, J.-Y., Zheng, Y.: Myers’ type theorem for integral Bakry-Émery Ricci tensor bounds. Results Math. 76 (1), Paper No. 32, (2021).
  • [5] Petersen, P., Wei, G., Relative volume comparison with integral curvature bounds. Geom. Funct. Anal. 7 (6), 1031–1045 (1997).
  • [6] Ramos Olivé, X., Seto, S. Gradient Estimates of a nonlinear parabolic equation under integral Bakry-Émery Ricci condition, Preprint (2024).
  • [7] Seto, S., Wei, G. First eigenvalue of the p-Laplacian under integral curvature condition. Nonlinear Anal. 163, 60–70 (2017).
  • [8] Tolksdorf, P.: Regularity for a more general class of quasilinear elliptic equation. J. Differential Equations 51 (1), 126–150 (1984).
  • [9] Wang, Y.-Z., Li, H.-Q.Lower bound estimates for the first eigenvalue of the weighted p-Laplacian on smooth metric measure spaces. Differential Geom. Appl. 45, 23–42 (2016).
  • [10] Wang, L., Wei, G. Local Sobolev constant estimate for integral Bakry-Émery Ricci curvature. Pacific J. Math. 300 (1), 233–256 (2019).
  • [11] Wei, G., Wylie, W. Comparison geometry for the Bakry-Émery Rici tensor. J. Differential Geom. 83 (2), 377–405 (2009).
  • [12] Wu, J.-Y. Comparison geometry for integral Bakry-Émery Ricci tensor bounds. J. Geom. Anal. 29 (1), 828–867 (2019).
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Cebirsel ve Diferansiyel Geometri
Bölüm Araştırma Makalesi
Yazarlar

Shoo Seto 0009-0005-6276-7949

Erken Görünüm Tarihi 9 Nisan 2024
Yayımlanma Tarihi 23 Nisan 2024
Gönderilme Tarihi 13 Şubat 2024
Kabul Tarihi 1 Nisan 2024
Yayımlandığı Sayı Yıl 2024 Cilt: 17 Sayı: 1

Kaynak Göster

APA Seto, S. (2024). Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds. International Electronic Journal of Geometry, 17(1), 245-251. https://doi.org/10.36890/iejg.1436665
AMA Seto S. Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds. Int. Electron. J. Geom. Nisan 2024;17(1):245-251. doi:10.36890/iejg.1436665
Chicago Seto, Shoo. “Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds”. International Electronic Journal of Geometry 17, sy. 1 (Nisan 2024): 245-51. https://doi.org/10.36890/iejg.1436665.
EndNote Seto S (01 Nisan 2024) Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds. International Electronic Journal of Geometry 17 1 245–251.
IEEE S. Seto, “Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds”, Int. Electron. J. Geom., c. 17, sy. 1, ss. 245–251, 2024, doi: 10.36890/iejg.1436665.
ISNAD Seto, Shoo. “Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds”. International Electronic Journal of Geometry 17/1 (Nisan 2024), 245-251. https://doi.org/10.36890/iejg.1436665.
JAMA Seto S. Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds. Int. Electron. J. Geom. 2024;17:245–251.
MLA Seto, Shoo. “Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds”. International Electronic Journal of Geometry, c. 17, sy. 1, 2024, ss. 245-51, doi:10.36890/iejg.1436665.
Vancouver Seto S. Lichnerowicz Type Estimate for the $p$-Laplacian Under Weighted Integral Curvature Bounds. Int. Electron. J. Geom. 2024;17(1):245-51.
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