From The Volokh Conspiracy:

• Under the Supreme Court’s standard in District of Columbia v. Heller, knives are Second Amendment “arms” because they are “typically possessed by law-abiding citizens for lawful purposes,” including self-defense.
• There is no knife that is more dangerous than a modern handgun; to the contrary, knives are much less dangerous. Therefore, restrictions on carrying handguns set the upper limit for restrictions on carrying knives.
• Prohibitions on carrying knives in general, or of particular knives, are unconstitutional. For example, bans of knives that open in a convenient way (e.g., switchblades, gravity knives, and butterfly knives) are unconstitutional. Likewise unconstitutional are bans on folding knives that, after being opened, have a safety lock to prevent inadvertent closure.