Gray, A.; Willmore, T. J. Mean-value theorems for Riemannian manifolds. (English) Zbl 0495.53040 Proc. R. Soc. Edinb., Sect. A 92, 343-364 (1982). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 5 ReviewsCited in 27 Documents MSC: 53C20 Global Riemannian geometry, including pinching 53B20 Local Riemannian geometry 58C35 Integration on manifolds; measures on manifolds Keywords:function on a sphere; mean-value; harmonic functions; harmonic manifold; power series expansion; Pizzetti formula; Laplacian PDF BibTeX XML Cite \textit{A. Gray} and \textit{T. J. Willmore}, Proc. R. Soc. Edinb., Sect. A, Math. 92, 343--364 (1982; Zbl 0495.53040) Full Text: DOI OpenURL References: [1] DOI: 10.1007/BF02764713 · Zbl 0263.35013 [2] Copson, Proc. Roy. Soc. Edinburgh 60 pp 117– (1940) · Zbl 0027.26001 [3] DOI: 10.1112/jlms/s1-25.1.54 · Zbl 0036.23403 [4] DOI: 10.2307/2371513 · Zbl 0021.35503 [5] DOI: 10.1093/qmath/33.1.45 · Zbl 0509.53045 [6] Cartan, Géométrie des espaces de Riemann (1928) [7] DOI: 10.1007/BF02412767 · Zbl 0111.29901 [8] Brezin, Trudy Moskov. Mat. Obšč. 5 pp 311– (1956) [9] DOI: 10.1112/jlms/s1-22.2.101 · Zbl 0029.26602 [10] DOI: 10.1007/BF02786707 · Zbl 0332.35033 [11] Thomas, The differential invariants of generalized spaces (1927) [12] Berger, Lecture Notes in Mathematics 194 (1971) [13] DOI: 10.1090/S0002-9947-1981-0626485-6 [14] Besse, Ergebnisse der Mathematik 93 (1978) [15] DOI: 10.1007/BF02925426 · Zbl 0041.43801 [16] Ruse, Harmonic spaces (1961) [17] Ascoli, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Nat. 1 pp 1167– (1946) [18] DOI: 10.1098/rsta.1960.0008 · Zbl 0094.31901 [19] Ascoli, Pont. Acad. Sci. Comment. 7 pp 207– (1943) [20] Riemann, Gesammelt Werke (1876) [21] Pizzetti, Atti R. Accad. Rend. Cl. Sci. Fis. Mat. Natur. 18 pp 309– (1909) [22] Pizzetti, Atti R. Accad. Rend. Cl. Sci. Fis. Mat. Natur. 18 pp 182– (1909) [23] Olevsky, C. R. (Doklady) Akad. Sci. URSS 46 pp 3– (1945) [24] Olevsky, C. R. (Doklady) Akad. Sci. URSS 45 pp 95– (1944) [25] Olevsky, C. R. (Doklady) Akad. Sci. URSS 40 pp 5– (1943) [26] Olevsky, C. R. (Doklady) Akad. Sci. URSS 33 pp 282– (1941) [27] Lelong-Ferrand, Differential geometry and relativity (1976) · Zbl 0345.53028 [28] DOI: 10.1007/BF02391776 · Zbl 0163.16602 [29] Helgason, Differential geometry and symmetric spaces (1962) · Zbl 0111.18101 [30] DOI: 10.1007/BF02564248 · Zbl 0146.43601 [31] Günther, Ber. Verh. Sächs. Akad. Wiss. Leipzig 102 pp 1– (1957) [32] DOI: 10.1112/plms/s3-44.2.215 · Zbl 0491.53035 [33] DOI: 10.1007/BF02395060 · Zbl 0428.53017 [34] Gray, Michigan Math. J. 20 pp 329– (1973) [35] Godement, C. R. Acad. Sci. Paris 234 pp 2137– (1952) [36] Gelfand, C. R. (Doklady) Akad. Sci. URSS (N.S.) 70 pp 5– (1950) [37] Fusaro, J. Math. Mech. 18 pp 603– (1968) [38] DOI: 10.1090/S0002-9947-1961-0131839-8 [39] DOI: 10.1007/BF01782367 · JFM 56.0419.01 [40] Eisenhart, Riemannian geometry (1925) [41] Desertine, C. R. Acad. Sci. Paris 273 pp 164– (1971) [42] Courant, Methods of mathematical physics 2 (1962) · Zbl 0849.01022 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.