  The Fermi surface topology in the two-dimensional Hubbard model is
particularly relevant for the high-temperature superconductors, whereas its
theoretical research encounters with the difficulty of the analytical
continuation problem. To this end, we proposed the concept of the
momentum-dependent compressibility, defined as the variation of the momentum
distribution function with respect to the chemical potential. The surface
determined by the maximum of the momentum-dependent compressibility is nearly
identical to the Fermi surface in the weakly and intermediate coupling regions
according to our numerical results. In the correlated region, this surface also
exhibits pocket and arc features, just like the Fermi surface in
high-temperature superconductors. Therefore, for theoretical studies, this
surface can be used as an alternative to determine the underlying Fermi
surface. Considering that the momentum-dependent compressibility is closely
related to the charge density correlations, our work also shows a connection
between the Fermi surface topology and the charge density fluctuations.
