In 1904,[2] Herglotz defined relations for the
electrodynamic potential which are also valid in
special relativity even before that theory was fully developed.
Hermann Minkowski (during a conversation reported by
Arnold Sommerfeld) pointed out that the four-dimensional symmetry of electrodynamics is latently contained and mathematically applied in Herglotz' paper.[3]
In 1907,[4] he became interested in the theory of
earthquakes, and together with
Emil Wiechert, he developed the Wiechert–Herglotz method for the determination of the velocity distribution of Earth's interior from the known propagation times of
seismic waves (an inverse problem). There, Herglotz solved a special integral equation of Abelian type.
Gesammelte Schriften / Gustav Herglotz, edited for d. Akad. d. Wiss. in Göttingen by
Hans Schwerdtfeger. XL, 652 p., Vandenhoeck & Ruprecht, Göttingen 1979,
ISBN3-525-40720-3.[11]
Vorlesungen über die Mechanik der Kontinua / G. Herglotz, prepared by R. B. Guenther and H. Schwerdtfeger, Teubner-Archiv zur Mathematik; vol. 3, 251 p.: 1 Ill., graph. Darst.; 22 cm, Teubner, Leipzig 1985.
Über die analytische Fortsetzung des Potentials ins Innere der anziehenden Massen, Preisschriften der Fürstlichen Jablonowskischen Gesellschaft zu Leipzig, VII, 52 pages, with 18 Fig.; Teubner, Leipzig (1914).[12]
Über das quadratische Reziprozitätsgesetz in imaginären quadratischen Zahlkörpern, Ber. über d. Verh. d. königl. sächs. Gesellsch. d. Wissensch. zu Leipzig, pp. 303–310 (1921).
^Herglotz, Gustav (1907), "Über das Benndorfsche Problem der Fortpflanzungsgeschwindigkeit der Erdbebenstrahlen", Physikalische Zeitschrift, 8: 145–147