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Stereo matching recovers 3D scene information based on the correlation between corresponding pixels. Despite impressive progress, existing methods lack sufficient correlation priors in ill-posed regions such as occlusions, detailed and reflective regions. In this paper, we propose Geometry Aware Stereo Matching Network (GEAStereo) to enhance geometric structure perception and address this issue. We adaptively incorporate the Monocular Disparity Distribution Prior into the stereo cost volume, building Mono-Stereo Fusion Volume (MSFV), which effectively captures global geometric structures and rectifies the correlation information in ill-posed regions. Furthermore, we introduce rich detail information from gradient features and construct a Detail-Aware Volume (DAV) by aggregating the group-wise cost volume under the guidance of gradient spatial attention, thus enhancing the correlation modeling in detailed structures. Jointly, MSFV and DAV provide rich correlation priors for disparity iterative optimization. Experimental results show that our method achieves competitive results on the ETH3D and KITTI2015 benchmarks. Compared with the state-of-the-art methods, our method demonstrates stronger performance in zero-shot generalization. The code is available in Supplementary Material.